Pat the sea bass dry on all sides with a paper towel. Sprinkle with salt and pepper.
Heat the butter and olive oil in a nonstick skillet over medium-high heat. When the butter is melted and foamy, add the sea bass fillets skin-side down.
Cook the fillets undisturbed for 4-5 minutes, or until the skin releases easily and is golden brown.
Flip the fillets gently. Scatter the sliced garlic and lemon slices around the fish. Cook for another 3-5 minutes, spooning some of the pan butter over the fish, until it flakes easily with a fork or registers 140-145°F inside.
Remove from heat and let the fish rest for 1-2 minutes in the pan. Sprinkle with chopped parsley and a squeeze of lemon before serving.