Rinse fish thoroughly in cold water; pat dry, and set aside.
Melt butter in a small saucepan; stir in chopped parsley, and set aside.
Combine flour, salt, and pepper; dredge fish in flour mixture. Place fish on rack in a shallow broiling pan. Spoon half of butter mixture over fish.
Broil 4 inches from heating element 5 minutes. Remove from heat; using a spatula, carefully turn fish. Baste with remaining butter mixture; continue broiling an additional 5 minutes or until fish flakes easily when tested with a fork.
Serve immediately with lemon slices. Garnish with parsley, if desired.