Dice the tomatoes and gently press them with paper towels to remove excess moisture.
In a bowl, combine tomatoes, red onion, basil, 1/2 tablespoon olive oil, salt, and pepper.
Brush one side of every ciabatta slice with olive oil.
Arrange half of the slices oil-side down.
Layer mozzarella evenly over each slice.
Spoon the tomato mixture over the mozzarella.
Sprinkle Parmesan on top.
Cover with the remaining ciabatta slices, oil-side up, pressing gently.
Heat a grill pan or skillet over medium heat.
Cook the Bruschetta Grilled Cheese Sandwiches until golden brown on one side.
Flip carefully and rub the toasted side with the garlic clove.
Cook until the second side is crisp and the mozzarella has melted.
Transfer to a serving board, rub the remaining side with garlic, drizzle with balsamic glaze, and serve immediately.