Few Europeans — let alone Americans — could find the island of Bornholm on a map. It sits in the Baltic Sea, somewhere off the northern coast of Poland, but it’s actually Danish turf. This hidden outpost is Copenhagen residents’ version of the North Fork of Long Island: Unpretentious and relaxing, it largely consists of farms, rolling countryside and goldenrod-colored, timber-framed houses.

The quiet towns that dot its coasts are a startling contrast to the gleaming Danish capital, which is half an hour away by plane (about $200 round-trip on Danish Air Transport).

Bornholm is full of winding streets and harbors where small sailboats bob in the water. It’s a longtime weekend getaway spot for weary city dwellers, lured by the balmy climate — with better weather than most of the mainland, it’s nicknamed the Sunshine Island.

These days, it’s not just the weather that’s drawing visitors: It’s the food. Thanks to restaurants like Noma, Denmark is arguably already the crucible of new Nordic cooking. Bornholm, though, is those chefs’ secret weapon — or, more accurately, the secret sauce behind every menu.

The higher temperatures help grow apples and berries that taste sweeter. What’s more, the low salt content of the Baltic Sea (around 1 percent, compared with up to 5 percent in other bodies of water) means herbs, seaweed and other ingredients are tastier.

No wonder Copenhagen-based chefs quietly rely on Bornholm for ingredients. Nicolai Nørregaard is typical in that regard. One of new Nordic cuisine’s heavy hitters, he runs the Michelin-starred restaurant Kadeau in Copenhagen. Unlike his peers, Nørregaard grew up here, too, and today runs a farm, overseen by his father, that supplies produce for his kitchen on demand.

What’s more, every summer, Nørregaard shutters his city site and decamps full-time to the Sunshine Island, running a seasonal outpost of Kadeau in a converted beach shack where he once, as a child, used to come for fried chicken and ice cream. After a minimalist makeover that added an on-site garden and cozy fire pit, this Kadeau is a showcase for his unfussy but inventive cooking.

An 11-course tasting menu (around $170) could feature asparagus soup with gooseberries or pumpkin sprinkled with citrusy wood ants. Dishes are constantly reinvented from week to week to align with what’s fresh. “I learned a lot of the techniques from my granddad,” he says, smiling shyly. “But I don’t keep my recipes for some reason. I know it’s stupid.”

Kadeau sits on the southern tip of the island, where you’ll also find the best beaches. (The northern coastline is rocky, though the energetic swimmer can clamber into the ocean almost anywhere.) To walk off an overindulgent meal, stroll the wide swaths of Dueodde beach, which is reachable via a long boardwalk. It has a convenient parking lot and lots of cafés.

Nearby, many of Bornholm’s other foodie firms cluster on the east coast — in its sunniest corner — between the towns of Nexø and Gudhjem.

Stop in at the farm shop of Høstet, which uses the tangy, tangerine-like fruit of the wild-grown sea buckthorn in jams and cordials.

Then, try some of the extra-sweet wild strawberries in rolled ice cream at the Original Is van, parked on the harbor’s edge in a small settlement called Snøgebæk.

Don’t leave the island without tasting its signature dish, an irresistible mashup of egg yolk, rye bread and smoked herring known as Sol over Gudhjem or, literally, the “sun over God’s home.” You can order it almost anywhere, as herring is a longtime local delicacy, with dozens of smokehouses dotted around Bornholm. Sit on the harborfront terrace at the best smokery Gudhjem Rogeri on a sunny day.

Otherwise, opt for a glass of wine and a platter of smoked fish at the new, all-white Norresan housed in an erstwhile smokery, which nurse Pernille Funch and her husband Peter overhauled last year to open this Scandi-chic café.

Licorice vies with herring to be Denmark’s national dish, so of course there’s a noteworthy licorice-maker on Bornholm, too. Local boy Johan Bulow started out cooking in his mother’s kitchen, workshopping a recipe that barely resembles a handful of Good & Plenty; he now exports his gourmet riff on licorice worldwide.

Though Bulow has abandoned his original factory on the island for a handier site near Copenhagen, you can still visit his former HQ in Svaneke — and sample its wares before you buy. Whether coated in chocolate or spiked with cranberries and chili, this dessert is salty, sweet and addictive.

Flights from Copenhagen are so frequent that you could make a day trip to the island, but it’s best to stay the weekend so you can consume as much of the delicious grub as possible. To do so, book a room at Nordlandet (from $185) on the northern side. Once a kitschy former motel, it got a modernist redo last year by Kadeau’s Nørregaard and his team. Note the witty sign painted onto the rocks around two nearby inlets: “Pool,” it reads, with dry Danish wit. Only the brave should take a dip, though: even on the Sunshine Island, the Baltic waters remain bracing year-round.

The author was a guest of Visit Denmark.