Heat grill. In small bowl, combine garlic and 1 tablespoon of the steak sauce; mix well. Set aside.
Add enough broth to reserved mushroom liquid to make 3/4 cup. In small saucepan, combine remaining 2 tablespoons steak sauce, broth mixture, mushrooms and cornstarch; mix well. Cook over medium heat until mixture comes to a boil, stirring occasionally. Boil 1 minute. Remove from heat. Stir in parsley. Cover to keep warm.
When ready to grill, place steaks on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Brush with garlic and steak sauce mixture. Cook 7 to 12 minutes or until of desired doneness, turning once and brushing with garlic and steak sauce mixture. Serve steaks topped with mushroom sauce.