Let fish sit in a colander at room temp for at least 30 minutes to drain any liquids and reach a moderate room temp.
Meanwhile, make the sauce: Heat butter, shallots, and garlic in a large frying pan and cook on medium heat, stirring often, 2 min. Add wine and lemon juice and bring to a boil. Boil until sauce thickens slightly, 2-3 min. Stir in parsley and lemon zest. Season with pinches of salt and pepper to taste. Cover and keep warm.
Using paper towels, pat dry the fillets to remove as much moisture as you can. Sprinkle a light layer of kosher salt and black pepper over both sides of each fillet. In a large nonstick frying pan over medium heat, add 3 TB olive oil. Arrange 2 fillets in the pan and cook with lid ajar to allow steam to escape. Cook about 3-4 min or until bottoms of fillets are browned. Flip carefully and brown other side 3-4 min (keep in mind that if your fish is less than 1 inch thick, you’ll need to adjust for less cook time.) You want the fish just cooked, but not over-cooked. Repeat with other 2 fillets (unless your frying pan is large enough to cook all 4 fillets without crowding, it’s best to cook in batches; otherwise, the fish will be more steamed than browned.)
Plate the fish fillets and pour warm sauce over them. Serve immediately.