Rinse fish thoroughly in cold water; pat dry. Rub fish with oil, 1/2 teaspoon salt, and paprika; place on well-greased rack in a broiler pan. Broil fish 5 to 6 inches from heating element 5 minutes; turn fish, and continue broiling an additional 5 minutes or until fish flakes easily when tested with a fork. Remove fish to a serving platter, and keep warm.
Combine butter, lemon juice, parsley, remaining salt, and pepper in a small saucepan. Cook over low heat until butter melts, stirring occasionally.
Pour butter sauce over reserved fish. Garnish with lemon slices, and serve immediately.