Heat gas or charcoal grill. Place vegetable burger on grill over medium heat. Cover grill; cook 6 to 9 minutes, turning once, until thoroughly heated.
Divide mushrooms evenly onto patties; top with cheese. Cover grill; cook 1 to 2 minutes longer or until cheese is melted. Spread 1 tablespoon mayonnaise on each bun. Serve patties in buns with tomatoes, lettuce, ketchup and mustard.