There's more to Danish cuisine than Noma. Out in the north Atlantic, Michael Booth finds a new Nordic frontier as Faroe Islands chefs raise traditional foods to new levels of pleasure

The weather looks as changeable as a toddler's tantrums. Thank god we're not in a helicopter, I think to myself as the plane banks on its final approach and a cluster of snow-covered island-mountains erupting from the sea loom through the storm clouds.

This Nordic Hawaii is the Faroe Islands. Forget Copenhagen, or even Reykjavik, I'd heard this cluster of 18 rocky islands in the middle of the north Atlantic, inhabited by 50,000 descendants of Norse renegades, is the new frontier in the new Nordic food movement. A place where a tiny band of determined pioneers, led by one visionary chef, is developing a radical, contemporary cuisine from the most meagre culinary heritage.

An hour or so after landing, it seems I spoke too soon about the helicopter: it is the only way to reach the island of Stóra Dímun, home to a couple of hundred sheep and the Petersen family's farm, my first destination in a three-day tour of the islands' nascent food scene. First challenge is to reach the helicopter which is idling on what is, essentially, an ice rink. With my arms occupied by luggage and a woolly hat, I am at the mercy of both natural and man-made gales. For every step forward I slide two back. In the end, a fellow passenger comes to my rescue and drags me backwards on my heels like a shop dummy.

I assume he is a birdwatcher, like so many visitors to the Faroes, but the duffle-coated samaritan turns out to be John Gynther from the experimental cheese division (really) of a Danish dairy products company, on his way to check on the progress of some cheeses.

The rugged terrain of the Faroe Islands. Photograph: Per Morten Abrahamsen

"The humidity here is perfect for maturing cheeses, but nobody has tried it before," he tells me. "If it's successful, I hope some of the best restaurants in the world will give it to their guests. It'll be the true taste of the north Atlantic, expressed in a cheese."

Arriving safely at the Petersen's farm, I hear a little about their lives. Their forefathers have farmed sheep here for over 200 years. That little black tar cottage over there is the children's schoolhouse; a teacher arrives every Monday and stays in the attic. And those chocolate dots inching across the sheer hillside are their sheep, whose coats have evolved a yeti-like shagginess over the centuries.

Jógva Jón Petersen shows us into the hjallur, a wooden shed with vented walls where the sheep carcasses are hung by their feet to dry in the wind, flayed like some macabre art installation. This is the Faroe's famous ræst mutton, he explains, semi-dried and fermented in the sea air. Dangling alongside is Gynther's cheese, which we taste in Jógva's low-ceilinged kitchen as his kids bring to the table their treasured toys and, at one point, a pet rabbit. The cheese is good, resembling a bitter manchego. The ræst is chewy like thick-cut pata negra ham, with a strong flavour only just the right side of "sheepy" for me.

That evening, in the islands' capital, Tórshavn, we eat in what appears to be a Hobbit dwelling but is actually a cosy, turf-roofed cottage housing a restaurant, Áarstova (dinner from about £55). We dip our heads to enter and are confronted with another dried sheep carcass flayed on a fancy, turned-wood stand. They're not squeamish, the Faroese – as evidenced by the annual summer pilot whale slaughter, the grindadráp, which apparently has something of a family festival air (though obviously not for the whales, which are slaughtered despite being so riddled with mercury that since 2008 the island's medical officers have recommended they are no longer considered fit for human consumption).

Diners outside Aarstova in Tórshavn

We are presented with a dør schnapps. This is my new favourite Faroese tradition: when arriving at a party or, sometimes, a restaurant, guests are presented with a glass of schnapps, refilled communion wine-style for new arrivals. We sit alongside a man called Mortan, who is one of life's enthusiasts. He insists we try some ræst mutton paired with amontillado sherry, and there is an unexpected repartee between the wine's oaky notes and the rich mutton. The geographical connection is not all that tenuous either, Mortan points out, given that for centuries the Faroese exported salt cod to Spain.

The talk turns to the islands' long-mooted independence from Denmark and the oil that many believe lurks offshore and could lift the Faroes' economy – which as far as I can make out is kept afloat by the Sarah Lund sweaters, made here by Gudrun and Gudrun, a company founded and run by two Faroese women, and sold in a shop on the harbourfront. As the schnapps bottles are drained, the tables are cleared for traditional dancing … national dress optional.

The next morning the Faroes fling another of their elemental challenges at us. We are to rendezvous at sea with the island's most highly prized catch: langoustines. From my room in the surprisingly hip Hotel Føroyar on the hillside above the capital, the sea looks more white than blue and I prepare to disgrace myself with all manner of uncontrollable bodily eructations as our boat heaves and plunges out into the fjord. A harrowing hour or so later, we come within hollering distance of our fisherman. He is bucking like a bronco in his bathtub boat, yet manages to toss us a live langoustine the length of my forearm. One of our party rips its plump, still-twitching tail from its body, and passes it to me to suck its ocean-sweet flesh. For a moment I forget the motion of the boat.

The langoustines make an appearance that evening, cooked this time, during a meal that evokes the food traditions we have seen over the past two days, yet also referencing the avant-garde kitchens of Denmark and Spain. Already on the table when we arrive, for example, is a large, dried cod's spine – a memorable piece of gastronomic melodrama that serves as a rack for crispy fried cod skins.

Stream running alongside traditionally built houses in the Faroe Islands. Photograph: Kimberley Coole/Lonely Planet/Getty

The foraged herbs, driftwood plates and powdered seaweeds are all recognisable New Nordic themes but I haven't eaten like this anywhere else in the world: this is food born from a survival imperative, refined for pure pleasure. We're at Restaurant Koks (from £50 for four courses), a name unfortunate to English ears, though the word is Faroese for flirt or fusspot. All the produce, bar the odd dash of white wine or vanilla, is harvested, caught, shot or cultivated on or around the islands.

"My cuisine is a mirror of the nature of the Faroes," chef Leif Sørensen tells me after the meal.

I first met Sørensen when he gave a talk at the MAD food festival in Copenhagen in 2012 that left the audience awed by his myriad, self-imposed challenges. Sørensen, a serious man of few, but well chosen, words, explained how he had returned to the Faroes after working in Michelin-starred kitchens in Copenhagen, wanting to discover what his home islands had to offer. On this evening it included the most blueberry-ish blueberries I'd ever ever tasted; sweet, soft deep-sea mussels; wild angelica; and a parade of dried shrimps whose super-intense flavour haunts me (in a good way) to this day.

"I kind of had to live up to my own manifesto," Leif told me, referring to 2004's now famous New Nordic Manifesto, of which he was a signatory. "The ambition was to do something different, to make it possible to eat a little better food here, to try to change the restaurant environment. It was difficult to get raw materials because they weren't allowed to sell the lamb or fish to restaurants. It was hopeless. I started to go out and collect plants, and that was the beginning."

Koks restaurant in Tórshavn

There was virtually no restaurant culture on the Faroes before Leif started Koks five years ago: it was illegal to serve alcohol in restaurants until 1992. But, slowly, new places are emerging in its wake, such as sushi restaurant Etika (from about £25), which uses only locally caught fish, and the restaurant at the Hotel Hafnia (three courses £50).

There's a new artisanal brewery, Okkara, and an increasing number of food events. For example, at the Faroe Bank Cod dinner at Áarstova every March, the Faroese Fisheries Laboratory's research annual catch of this otherwise protected species is cooked and served. By all accounts (OK, mainly Mortan's), it is the finest cod in the world.

The locals were sceptical about Koks at first. Some were aghast that their subsistence ingredients, such as ræst and puffin, were being served for foreign visitors. But Faroese now make up around half of Koks' guests, the rest coming mainly from Scandinavia, but also growing numbers from as far afield as Japan and Brazil.

Yet, as Leif tells me wearily, the challenges of running an avant garde restaurant on the fringes of the Arctic remain borderline insurmountable, and aren't limited to produce supply chains. "My staff can earn twice as much catching fish as they can cooking it," he sighs, looking more exhausted than any man I have ever seen.

Frankly, the Faroes are exhausting. But they are also exhilarating. I hear they appear through the mists from time to time, like Brigadoon. Next time they do, you should go.

• The trip was provided by the Faroe Islands tourist board (visitfaroeislands.com) and Hotel Føroyar (+298 31 75 00, hotelforoyar.fo, doubles from £205). Atlantic Airways (atlantic.fo) flies to Vágar, twice weekly from Gatwick, from £250 return

Michael Booth's book, The Almost Nearly Perfect People: The Truth About the Nordic Miracle, will be published on 6 February by Jonathan Cape, price £12.99. To buy a copy for £10.39 with free UK p&p call 0330 333 6846 or visit guardianbookshop.co.uk