Pat the halibut dry with paper towels and season with kosher salt and black pepper. Let sit for 5 minutes.

In a large skillet, heat 2 tablespoons of butter and 1 tablespoon of olive oil over medium-high heat until foaming.

Add halibut fillets to the skillet, skin-side down, and cook for 4-5 minutes. Flip and cook for another 3-4 minutes until flaky.

In the same skillet, add minced garlic and sauté for 30 seconds. Pour in ½ cup of white wine and scrape the pan.

Add the juice of 1 lemon, capers, and lemon zest. Stir and cook for 1-2 minutes to meld flavors.

Stir in 1 tablespoon of butter until melted. Return halibut to the skillet and spoon sauce over it. Cook for 1 more minute.