Pat the halibut fillets very dry with paper towels. Sprinkle the top side with a small amount of kosher salt.

In a large skillet, melt 2 tablespoons of butter with the olive oil over medium heat.

Once the butter begins to slightly brown and sizzle, add the halibut fillets to the pan, top side down. Sprinkle the back of the fish with the remaining salt and pepper.

Cook undisturbed for 5 minutes. Carefully flip the fillets using a fish spatula.

Add the lemon slices to the pan alongside the fish. Cook for an additional 3 to 5 minutes until the fish is opaque and flakes easily.

Transfer the fish and the lemon slices to a warm platter.

Pour the cooking fat into a small bowl. Let the burnt bits settle, then skim 2 tablespoons of the clean fat back into the skillet.

With the heat still at medium, add the chopped garlic and cook for 1 minute until fragrant.

Pour in the white wine and stir, allowing it to simmer and reduce slightly.

Stir in the lemon juice, capers, and parsley. Cook for 1 minute.

Remove the skillet from the heat and whisk in the remaining 2 tablespoons of butter until a glossy sauce forms.

Place the halibut back into the pan for 30 seconds, spooning the sauce over the top. Serve immediately with the pan roasted lemon slices.