Light the grill or heat the broiler. In a small bowl, combine the butter, anchovy paste, lemon juice, parsley, and a pinch each of salt and pepper.
Coat the tuna with the oil. Sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook the tuna for 4 minutes. Turn and cook until done to your taste, 3 to 4 minutes longer for medium rare. Top the hot fish with the flavored butter.