Preheat grill to medium high heat. Clean mushrooms and remove stems. Place caps on an oven safe grill pan with the gills face up. Grill for 8- 10 minutes.
Slice the mozzarella and tomato, and chop the basil. Top each grilled mushroom bottom with a slice of tomato followed by mozzarella. Place the grill pan under the broiler until mozzarella melts and bubbles. Remove mushrooms from pan and dress them with chopped basil and a drizzle of balsamic vinegar.