Cook rice in water as directed on package.
In food processor bowl with metal blade, combine cooked rice, black beans, mushrooms, onions, roasted peppers and garlic powder. Pulse to coarsely chop mixture. Add bread crumbs; pulse to mix. DO NOT PUREE.
Shape mixture into 4 patties, 1/2 inch thick; place on broiler pan. Broil 4 to 6 inches from heat for 10 to 12 minutes or until patties are thoroughly heated, turning once.
Place 2 pieces of cheese on each patty; broil an additional 1 minute or until cheese is melted. Place lettuce and patties in buns. Top patties with ketchup.