There’s a secret island in the Mediterranean. The volcanic island is filled with vineyards and farms, lined with black volcanic rocks, and surrounded by the blue-green sea. At least that’s what you’ve been told. A famous fashion designer has a home there. A famous singer rents a villa there. And famous movie stars like to vacation there. But they don’t want to share this secluded little paradise. Which makes you even more determined to find it.

Pantelleria is technically part of Sicily. The 32-square-mile island sits 62 miles southeast of Trapani and just 37 miles east of Tunisia. Given its strategic location, the island was captured and conquered many times over during its 35,000-year-old history. It’s been Italian since the end of World War II, though Arab influences can be felt all over the island.

After landing in Pantelleria Town, the small main port, board a boat to see the island from the water. The hilly, sun-baked island has fields of herbs, tomatoes, capers, and grape vines. Stone walls protect almond and lemon trees from the strong wind. Arab-inspired dammuso houses have thick stone walls and domed roofs. Steam spurts from thermal pools. Swimming spots are enclosed by black rocks. While gardens are filled with the overgrown remains of Roman buildings.

When the tour is over, stop at Cicci’s Bar near the main square for little sandwiches and a glass of vino bianco. Rent a moped to tour the rest of the island. Tools and pottery have been found at the Bronze Age village. Black Neolithic funeral mounds (sesi) are outside of Cunelie. Specchio di Venere is a crater lake inside of a dormant volcano. Natural saunas—those steaming thermal pools—are in caves at Monestero and Santaria. Vineyards are filled with Zibibbo grapes, which are used to make sweet wine. While the hike up Montagna Grande, the highest peak, is lined with maquis shrubs. Not that you’ll notice them once you see the view.

Back in Pantelleria Town, the promise of Prosecco lures you to another little bar. Though everyone seems to know each other, the people are welcoming and curious about how you discovered their island. Satisfied with your determined wanderlust, they direct you down the street to a little restaurant for dinner. There’s no sign, but the wonderful smell guides the way. Your stomach grumbles when more vino bianco is set on the wooden table. Penne with a thick pesto and just-picked tomatoes arrives. The pasta is followed by fresh fish with lots of garlic, parsley, and basil, plus potatoes drenched in olive oil and rosemary.

When you’re beyond full, it’s time to finally find your hotel. Resort Acropoli, which sits on a hillside near the Carthaginian Acropolis, overlooks the harbor and Pantelleria Town. The hotel was built on top of the ruins of an 18th-century palace. Your simple room looks like a traditional dammuso house. But you’re not quite ready to retire to it yet. Instead, you sit by the pool with a glass of sweet wine and watch the sun finish setting over the Tunisian mountains in the distance. No wonder no one wants to share this little island. Now, neither do you.