"We're looking for the hero's journey," David Gelb says. I'm sitting with him at a cellar table of three-Michelin-starred restaurant L'Arpège, in Paris, seven or eight courses through world-leading farm-to-table chef Alain Passard's vegetable-forward tasting menu. Gelb isn't telling me about his feature film The Lazarus Effect, released last year. In fact, the heroes in question aren't from any work of fiction. He's talking about chefs.

Gelb's Netflix original series Chef's Table, which premiered on the platform in 2014, is a game-changer. Not only for the food documentary format – which for decades had been based around former restaurant chefs travelling the world in search of food, or teaching people how to cook from the comfort of a studio kitchen – but also for the entire profession. That may seem grandiose, but the simple truth is that until Chef's Table, there had never been a documentary series that not only considered the what and the how of the chef, but the why, too.

If you've never seen it, each episode of Chef's Table is hinged around an intimate interview with a different industry-leading or notable chef, but it features a never-before-seen and often unflinching look into the way their restaurants work – including filming them during service. Each hour-long film reveals something about the dedication it takes on the part of the chefs in question to keep their restaurants performing at the very top level. But it also gets under their skin – revealing an insight into their way of working and, crucially, their reason for cooking.

Chef's Table creator David Gelb behind the camera at L'Arpège

David Gelb behind the camera at L'Arpège

Photograph by Lucie Cipolla / Netflix

Gelb explains to me that the process he and his crew of cameramen, directors and editors have landed on is to "make a plan, then show up, then throw out the plan". To make each episode, it takes ten days with each chef – that's all they have. And although Gelb is a feature film director, too, he can't script any part of the episode, save for rough ideas on motifs and locations he and his team discuss beforehand. "An easy explanation of this was the first episode that I directed, with Massimo Bottura," he tells me.

"We talked on the phone at length, to both him and Laura, his wife, and we came up with a plan of what we thought would happen. But Massimo is this spontaneous person, so on the first day when we were supposed to be doing a long interview, instead we got the feeling that he wanted to go to the Parmigiano shop – so that's exactly what we did."

The first two seasons feature, among others, Brazilian chef Alex Atala of D.O.M., supine on the back of a speedboat en route back from the Amazon, and Francis Mallman off-grid on an uninhabited Patagonian island. They also feature uncompromising looks into the personal traumas that some of these chefs have had to overcome on their journeys to the top, including the death of Gaggan Anand's brother; N'Naka's chef-patron Niki Nakayama being a gay woman in a socially conservative family; Dominique Crenn losing her adoptive father; or, in the most darkly ironic and profoundly emotional turn of the series, Grant Achatz of the great Chicago restaurant Alinea facing a battle with tongue cancer that left him having to learn to taste from scratch – at a point where his restaurant already had three Michelin stars. It's at times raw, at times poetic – its detractors may call it overblown – but it feels more real and immediate than any food television the world has seen before.

"Our job is to channel the passion of the chef," Gelb tells me. "We still make sure that we have what we need to make a film, but it kind of becomes a collaboration in that way, and that's the fun of documentaries. As we do interviews, we discover stuff about the chef that maybe previous journalists may not have realised or thought was that important. And some of the things we think are interesting, the chefs don't necessarily think are important, because a chef will look at his own life story a little differently than we might. So as we learn things, we adapt, and we have those ten days and there's a big responsibility to leave with a film, and that's the challenge that's put to the directors. It's capturing something that's honest, and complete within ten days, without faking it."

Gelb is, simply put, a filmmaker for whom food is a primary passion – he has a fanatical outlook towards the exemplary, frenetically paced and constantly morphing food landscape at the top level, and its ever-increasing absorption into mainstream culture. It's the same passion that's the reason millennials are spending more, in relative terms, on food and drink than the generations before them; the same one that means this magazine, and countless other regional and global food publications, are finding so many hungry readers.

Food is moving from a cultural commodity to a pop-cultural one; the visibility of the chef is at an all-time high, and shows like Chef's Table fuel the fire. But aside from someone of Gelb's obvious talent for narrative – first showcased in the feature-length documentary Jiro Dreams of Sushi, which found popularity and acclaim having been added to Netflix's roster after a limited theatrical release – the question remains: why had no one approached the food documentary in this way before?

I ask Gelb if he, or anyone else with his handle on narrative-driven documentary filmmaking, could have made something like it a decade ago. "I could barely make this type of show when we did make it," he replies. "People have been interested in chefs for a while, and food TV has been successful for some time now, but what I think we're doing is a bit different. Today's climate, or the appetite from audiences, is allowing a deeper, story-driven look at the chef's life, and they're not expecting or demanding us to explain the recipes and make it an instructional cooking show, which is the original tradition of cooking shows, starting with Julia Childs.

"It's a unique moment that the audience is accepting of it, Netflix was accepting of it – their gamble in us is paying off for them, because they found an audience for this type of programme that other networks didn't necessarily believe existed."

Food is moving from a cultural commodity to a pop-cultural one; the visibility of the chef is at an all-time high

A significant factor in its production is the relative lack of technological limitation in the mid-2010s. The turn of the millennium heralded in digital filmmaking to the mainstream – filmmakers can now achieve a cinematic look and feel with smaller and lighter cameras than ever before, sometimes even with a DSLR camera that an aspiring amateur could easily afford. "Technology allows us to do this at a much less expensive cost than it would have been ten years ago," Gelb says. "To shoot at that kind of quality then, you'd have had to shoot it on 35mm film." If it seems a minor point, think of the size of a traditional Hollywood film set, then think of a restaurant kitchen. Until digital filmmaking's equipment began to shrink, one camera would have struggled with filming one service, let alone multiple.

With lightweight cameras creating beautiful images, the vibrant, artful plates created by Chef's Table's subjects come to life. But the technology also allows the viewer a sense of first-hand experience: you're at the pass with the chefs, but it also takes you inside the dining room. It's a sense of immersion that's only recently become a possibility – and one that's as close as most of its audience will get to eating at some of the world's most iconic restaurants. Chef's Table offers the viewer a real, nakedly genuine glimpse of these chefs' jobs, and of their personalities, both during the tension of the service and in the chefs' accompanying monologues, too.

Gelb describes a moment in every episode's production where the chef – exhausted by long hours of interviews in addition to neverending restaurant services that have to work around a camera crew – breaks down a wall. Positively or negatively, there are moments where the chef reveals something they haven't before, at least not publicly. Almost universally, these insights reveal the real story ingrained in the interview; the reason why the chefs devote themselves to cooking.

Dan Barber – chef-patron of two of only a few restaurants than can compare to Passard's in terms of their influence on the farm-to-table movement, Blue Hill and Blue Hill at Stone Barns in New York – felt a touch ambivalent about the prospect of the show before filming. He, like many of the chefs in the first and second seasons, is a decorated, world-renowned chef with a restaurant in the World's 50 Best list – at this level, these chefs are not unused to media attention and interest.

"When you're filming for ten days, what you don't know when you're going into it is that you get worn down," he says. "Chefs get very good at saying what they want to say in interviews, but after a third full day of filming you can't do that. That's in part because the series is well funded, and they have the opportunity to take their time – but what you get is a truer sense of the person. I didn't anticipate that going in, but that's exactly what happened."

After two successful series that traverse LA, New York, San Francisco and Chicago, as well as Bangkok, Mexico City, São Paolo, Patagonia, Melbourne, Modena and Kobarid, Slovenia, there's a notable absence of one particular culinary destination. The world's most fabled food nation, Gelb explains, wasn't the most straightforward when it came to planning episodes.

"France is such an important destination when it comes to food," he says. "Traditionally the most important, internationally. Other countries have certainly planted their flags in the ground and become incredible landscapes for food as well, but historically France is the mecca.

All of our chefs had gone to France to train, so we wanted to do something special for it

"We hadn't had a single French chef in the first two seasons with the exception of Dominique Crenn, but she's really an American at this point. All of our chefs had gone to France to train, so we wanted to do something special for it. We couldn't do one episode to represent the entire country, so we wanted to do four chefs with different approaches, different stories, different places in the landscape of French cooking."

The result is a four-part season showcasing four chefs who represent the changing face of modern French cooking. The first episode is the reason I'm sitting at the vaunted long table in L'Arpège's ground-floor dining room – thrillingly, for the geek in me, at the same table that makes up the title shot of the series – it's about Alain Passard, the restaurant's chef-patron. Passard is "the man", according to Gelb – someone who took an unfashionable restaurant space in the septième arrondissement in Paris in 1986, and won his third Michelin star ten years later. "L'Arpège got three stars in a space that was considered impossible to get three stars in," Dan Barber says. "I found that to be really thrilling, that at a lower budget and in a smaller kitchen and space, he could perform at the very highest level."

But not only that, he's a restless personality, a shapeshifting schemer who's on the lookout for ways to push the button, as evidenced by the notorious decision in 2001 to remove meat and fish from his menu entirely. It was a decision that shocked the French restaurant world. There was a sense of provocateurship in there; but it was one that was made to show the world that farm-to-table dining and haute cuisine could coexist. One of our courses at L'Arpège consists entirely of a lightly roasted carrot wrapped in a thin slice of rhubarb.

It's a dish so simple and ingredient-led as to be a statement in itself. "The fact that he ushered vegetables centre-stage, in a three-star, haute-cuisine context – that was pretty big," Barber says. "He took it a step further, and in a way that was so bold and so iconoclastic. I found that thrilling, because he had a lot riding on it." Passard owns three farms on the outskirts of Paris, and cooks dishes that are indelibly tied to what the landscape provides him. His influence and skill comes from a tireless commitment to cooking sustainably and seasonally. But despite his profile, he has not often sought out the limelight.

He comes out towards the climactic courses of our tasting menu to talk about his participation in the project, and is warm, pensive, effusive, and candid – as he is throughout his episode. He describes the chance to take part in Chef's Table as a "heavenly gift from David."

"I declined lots of TV shows because I didn't think I'd learn anything," he says. "With David, I got the chance to learn about myself."

Chef's Table: France

Creator David Gelb on the show's all-French season

Chef's Table's third season features four different French chefs: Alain Passard of L'Arpège, Adeline Grattard of Yam'Tcha, Alexandre Couillon of La Marine and Michel Troisgros of Maison Troisgros.

"Through Michel Troisgros's story we were also able to tell the story of his father and grandfather, the tradition of the Troisgros brothers and nouvelle cuisine," Gelb says, "and this very important backstory in French cooking.

"Then Alain Passard is an incredibly charismatic character – who risked everything for the sake of creativity, has no other restaurants, who's incredibly passionate, and who revolutionised the way we look at vegetables.

"Adeline Grattard and Alexandre Couillon represent two branches of a newer wave of French cooking. Alexandre Couillon uses a lot of Japanese fish preparation techniques, but making it a style that's very specific to his home in Noirmoutier-en-l'Île – a place where fine dining was not a priority. It's a great love story between him and his wife Celine.

And then you have Adeline Grattard, who has a bit of a love story herself – she and her husband created this Chinese/French fusion that's incredibly elegant, and respected by both Chinese and French chefs around the world."

Considering French cooking has occasionally been accused of having a stubborn approach to sweeping change, the four chefs are all incredibly progressive. "We were trying to find different chefs, at different places in their careers," Gelb says, "different places in the history of French cooking.

"We don't say that it's a complete spectrum of French cooking, because there's so much to it, but it's a start."

Passard's response to his episode is one that's not necessarily universal – as Gelb says, "Some chefs say 'thank you', some say 'you're welcome'. We've had the whole spectrum of reactions." It's logical when you consider that each episode is essentially a character study, and often a very personal one at that. It's what happens when food is approached through the eyes of someone more closely inspired by Planet Earth than the Food Network. "We don't really consider our show intellectual as much as we consider it emotional and character-driven," Gelb says.

"The concepts of some of the episodes are more heady than others. The Dan Barber episode, for instance, that's certainly more of an intellectual episode, because he is a food intellectual in a lot of ways, as well as a chef. And then the Alain Passard episode is quite emotional."I had a hunch that people wanted to watch a more beautiful type of documentary when I watched the BBC series Planet Earth. It gave me the idea that there's room to make a beautiful show about food – one that goes beyond the type of instructional or reality television show you'd normally see on TV."

For Gelb, the relative lack of constraints the Netflix medium provides is crucial to the show's success. Chef's Table doesn't have to rely on grabbing the attention of channel-hoppers, nor does it have to attract advertisers. Because Netflix doesn't publicly release viewing figures for its shows, its original programming is allowed to be a slow burn. "Netflix allows us the time to build our audience, without having to immediately pander to an existing one," Gelb says. "That's why our show is able to exist."

That's not to say that each episode is a freewheeling video essay – in fact Gelb's story-led approach makes it incredibly accessible. "There are consistencies to the narrative structure," he says. "Our job is to make that structure invisible." The result is a set of deeply character-driven documentaries that a viewer can enjoy whether or not they're particularly interested in food.

Which brings us back to Gelb's "hero's journey archetype". Whether or not you believe chefs should be held up as cultural icons, Chef's Table, with its orchestral crescendos, sweeping camera movements, vivid colour palettes and mastery of storytelling, makes it easy to buy into the idea. As Gelb says, "We're choosing chefs who are heroes already. We're just trying to tell their story in a way that's inspiring."

Watch Chef's Table: France on netflix.com now