Pat fish dry. Season with ½ teaspoon salt and ¼ teaspoon pepper. Dredge in flour, and knock off excess. Set aside.
Heat oil and butter for the fish in a 12-inch heavy skillet over medium-high heat until foam subsides. Add fish and cook, turning halfway through, until browned and cooked through. This will take about 2-3 minutes total. Do not overcook.
Transfer fish to a plate. Discard fat from skillet and reduce heat to medium-low.
Add butter, and cook until browned, about 3-5 minutes. Remove skillet from heat and add parsley, lemon juice, and lemon zest. Stir to combine.
Pour sauce over fish. Serve with lemon wedges.
