Pat the Chilean sea bass fillets dry with paper towels and season both sides with salt and black pepper.

Heat 1.5 tablespoons of butter and 1.5 tablespoons of olive oil in a large skillet over medium-high heat until the butter is melted and foaming.

Place the seasoned fillets into the skillet skin-side down and sear for 3 to 4 minutes until the skin is golden brown.

Gently flip the fillets and cook for another 3 to 4 minutes, ensuring the fish is cooked through to an internal temperature of 140-145ºF.

In a small saucepan, melt 2 ounces of butter over medium-low heat until light brown, then stir in lemon juice, salt, and pepper.

Drizzle the lemon butter sauce over the cooked Chilean sea bass and serve immediately.