Preheat broiler to high and set oven rack to second-highest position. Line a baking sheet with heavy-duty foil.
Mist mushroom caps with cooking spray and sprinkle with salt and pepper. Place on baking sheet and broil until softened and browned, turning once, about 10 minutes total. Place a slice of cheese on rounded side of each cap and broil until cheese is bubbling.
Place a lettuce leaf and a tomato slice on bottom half of each bun. Top with a mushroom cap and other half of bun. Serve immediately.