Mix the butter, anchovy paste, lemon juice, parsley, and a pinch each of salt and pepper and place in the freezer.
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. Add the flavoured butter to the hot Tuna and serve.
Fish Alternatives: The lemon anchovy butter would also be very good with grilled halibut, swordfish or salmon steaks.