Rub pepper over meat. Place meat on the unheated rack of a foil-lined broiler pan. Broil 4 to 5 inches from the heat until desired doneness, turning once. Allow 10 to 12 minutes for medium rare (145°F) or 12 to 15 minutes for medium (160°F).
Meanwhile, in a saucepan, cook mushrooms, onions, and garlic in hot butter until vegetables are tender. Stir in cornstarch. Add vegetable juice and beef bouillon granules. Cook and stir until thickened and bubbly. Cook and stir 2 minutes more. Keep warm while cooking meat. Serve the sauce over meat.