Begin by thoroughly drying the sea bass fillets with paper towels. Season them evenly with salt and pepper on both sides.
Place a large skillet over medium heat and add the olive oil and unsalted butter. Once the butter has melted and the oil is hot, lay the sea bass fillets in the pan, skin side down. Cook them for approximately 3 minutes on each side, until they are golden brown and cooked through.
Carefully remove the fish from the skillet and set it aside on a plate.
In the same pan, add the minced garlic, dry white wine, and lemon juice. Stir well and allow the mixture to come to a gentle simmer. Reduce the sauce by letting it cook for about 5 minutes, ensuring it thickens slightly and the flavors meld together.
Finally, pour the fragrant white wine sauce over the cooked sea bass fillets and garnish with fresh parsley before serving.