"LOOK AT THAT!" Jamie Oliver says.

He’s holding his phone up to my face, and what I see on the cracked screen is very strange. It’s a picture from the Internet of two horned sheep with fleece so thick and matted that they might easily be mistaken for a pair of woolly mammoths. The sheep are native to Scotland, but you won’t find them scampering about the Highlands. In the picture, in fact, they are standing on a driftwood-strewn beach a few steps from the waterline.

They’re known as North Ronaldsay sheep, and they’re partly feral, as the 36-year-old British chef, activist, and TV star explains with the kind of excitement you’d see in a schoolboy pitching his first tent in the woods. The sheep wander the shores of the northernmost of the Orkney Islands. But what interests Oliver most about the beach-roaming beasties is their diet. “They only eat seaweed, so their nutritional content is through the fucking roof,” he says. “Because seaweed is the superfood of the world, pretty much.”

Not long ago, Oliver became so enraptured by the existence of these kelp-gobbling creatures that he embarked on a small-plane quest to sparsely populated North Ronaldsay, where locals butchered and prepared one of the sheep for Oliver. Whisky was involved, naturally, as was a proper Scottish roast. “It was amazing,” he says.

As he tells the story, Oliver is sitting by a window overlooking the streets of New York City in a communal space at Soho House, a private club in Manhattan’s Meatpacking District that’s a magnet for young, willowy beauty and square-jawed ambition. Oliver’s the most famous person in the room, but he’s also the one who comes off like a feral sheep in a stable full of thorough­breds. Unglamorously dressed in jeans and a flannel shirt and looking very much like the sleep-deprived father of four that he is, Oliver speaks in meaty, unruly chops of language that are heavily seasoned with conversational salt. He can be funny and charming, especially when he’s presiding over a press conference or flirting and ­bantering with a group of young agricultural pioneers at, say, an organic rooftop garden in Brooklyn. But his is a pugnacious strain of charm—that of a bloke who could be found dicing vegetables and pulling pints in his family’s Essex pub long before he was old enough to drive.

“You’d be wrong,” he says, “to think that I am slick or professional.”

A decade or so ago, Oliver became the Naked Chef, a tousle-haired, scooter-riding, drum-pounding chap who got famous and made a fortune with a cooking show (airing on the Food Network in the U.S.)—and then a flurry of cookbooks—that helped convince a new generation that it was cool to make a perfect roast chicken. The global foodie movement was turning young, iconoclastic chefs into rock stars, and Oliver was suddenly the scene’s Billie Joe Armstrong.

Oliver could by now have slipped into the lucrative routine of a celebrity chef: open another restaurant, crank out another cookbook, host a giddy game show involving elaborate cupcakes. Instead, much to his own surprise, he’s become a polarizing advocate for something that, on the surface, wouldn’t seem to need a whole lot of advocacy: he wants people, especially children, to eat better food.