Brush mushroom caps with pesto, using about 1/4 cup, and season with salt and pepper.
Brush olive oil onto grill, then heat grill to medium heat.
Add mushrooms to grill and cook 5 minutes with rounded side down.
Flip over, then add mozzarella to on top of mushroom caps.
Close grill and cook another 4-5 minutes, until cheese is melted.
Put buns on grill for about 1 minute to lightly toast.
Spread 1 tbsp pesto on each bun.
Top with mushroom caps and tomato slices.