On my first visit to the Michelin-starred restaurant Kadeau, on Bornholm, in 2017, the evening began the way many Danish dinners do: in the garden where the restaurant grows its produce, sipping a glass of sparkling natural wine. Standing among the bright bushels of kale and kohlrabi, co-owner and chef Nicolai Nørregaard shared his view of the island. “We chose Bornholm because it has so much to offer. It was untouched territory,” he said, dressed head to toe in black. Looking around the garden, with the sun streaming through the tall pine trees, I was inclined to agree. In recent years, many have been lured to this 227-square-mile island thanks to Kadeau, which offers a fine-dining experience in a converted old seaside cafeteria with simple, slatted walls and wraparound windows. In the wake of its success, a string of other small businesses has arrived, attracting the Copenhagen glitterati and other assorted visitors from all over. —Mary Holland