Sprinkle salt and pepper on both sides of each fillet. Place fillets, skin side down, in the center of a wooden plank or large ovenproof platter; dot with 2 tablespoons butter. Spoon potatoes around edges of fillets.
Broil fish and potatoes 5 to 6 inches from heating element 10 minutes or until fish flakes easily when tested with a fork and potatoes are lightly browned. Remove from oven, and dot fish with remaining butter. Sprinkle with parsley, and garnish with lemon slices. Serve immediately.