After a handful of trips to Iceland, you feel like you’ve conquered the country. The island isn’t that big, after all. You started in Reykjavík and the Golden Circle, of course. You drove the Ring Road, stopping in Vík and Akureyri, at glaciers and hot springs. Then you went off the main road to explore the Snæfellsnes and Westfjords peninsulas. Now it’s time to dig even deeper.

You’re on a ferry bound for the Westman Islands. The 15 volcanic islands—plus at least 30 more rock piles—sit off the south coast of Iceland. They’re all uninhabited, save for a handful of fishing cabins and millions of puffins, except for Heimaey. The largest island was first settled by runaway Gaelic slaves. Today, it’s home to Eldfell (a still-active volcano), a small airport, and a challenging golf course. But you’re here to eat at one of the best restaurants in the country.

Slippurinn (the Shipyard in Icelandic) is easy to spot when you arrive on Heimaey. It’s in a white concrete building from 1912 that housed the oldest machine workshop on the island. When the workshop closed 30 years ago, fishing equipment moved in. Many of the leftover tables and tools are now part of the seasonal, family-run restaurant.

You arrive to find a casual, nautical-themed lounge for a pre-dinner drink. The sofas look comfortable, but you opt for a high table, from which you can watch the kitchen in action. After looking over the beer list, which features 20 Icelandic brews, you keep an eye on the chef, who worked at award-winning restaurants in New York City before returning to Iceland. He’s using traditional techniques from fermenting and pickling to salting and smoking. Vegetables were picked on farms on the south coast, just a few miles away. Wild herbs and seaweed were collected nearby. While the fish comes straight from the market next door. It doesn’t get more local than this.

Though dinner is offered à la carte, you opt for the Fish Feast menu to sample local specialities. You start with dried cod flakes with brown butter and pickled pulse (dried seeds). You can smell the lobster soup, topped with whipped cream and parsley oil, long before it reaches your wooden table. While the addition of horseradish makes you wish for another helping of the salted cod croquettes. It’s a good thing you don’t ask for more. The fish of the day, a lemon sole, leaves you beyond stuffed. Thank goodness dessert is only skyr (Icelandic yogurt) and sorrel with toasted oats. There’s no way you could handle something sickly sweet right now.

As you finish the last sips of your wine—the only thing that hasn’t been local this entire meal—you stare out the window toward the harbor, a volcano, and the dark ocean. Iceland has become one of your favorite destinations in the world. It may be a small country, but there are plenty of gems like Slippurinn that you’ve yet to find.