Begin by preheating your grill for indirect cooking at 400 degrees F.
Cut off the top of the tomatoes and a small slice off of the bottom of the tomato to make it stand up without rolling around. Use a spoon to clean out most of the seeds from the inside of the tomatoes without breaking through the skin or bottom.
Season each tomato with salt and pepper and stuff about 1 oz of the fresh mozzarella into the tomato.
Wrap each tomato in a slice of bacon and secure with toothpicks. Place the wrapped stuffed tomatoes onto a vegetable grill pan and onto the grill.
Grill for 25 minutes, checking regularly to make sure the tomatoes are cooking evenly. The tomatoes will be done when the bacon is golden and the cheese is bubbling. Remove to a serving platter.
Garnish the grilled tomatoes with the balsamic glaze and fresh basil leaves. Serve immediately while the cheese is still warm and melty inside.