- Thoroughly combine ground beef, 1/4 cup teriyaki baste & glaze and pepper. Shape mixture into 4 oval patties.
- Sauté mushrooms and onion in hot oil in large skillet over medium heat 7 minutes. Remove from heat and stir in 2 Tbsp. teriyaki baste & glaze; keep warm.
- Cook patties on grill 4 to 5 inches from hot coals 6 minutes. Turn over and top each patty with 1 cheese slice; cook 5 minutes longer, or until thoroughly cooked. (Or, broil patties 5 minutes on each side, or until thoroughly cooked, topping with cheese during last 30 seconds of cooking time.)
- To serve, divide mushroom and onion mixture equally on bread slices; top with patties.