Heat butter and olive oil in a skillet large enough to hold the fish fillets over medium heat.
Pat fish dry with paper towels. Season well with salt and pepper. Dredge lightly in flour. Place them in the skillet. Cook for 3 minutes. Turn carefully with a spatula. Add lemon zest and juice to the skillet. Cook for 4 minutes.
Remove to a warm serving dish. Sprinkle with parsley. Place a slice of lemon on top. Serve immediately.