Add the tomatoes to a dry nonstick skillet and heat them until the outside begins to lightly char. Lower the heat, add one tablespoon of butter, and stir carefully.

Gently press the tomatoes with the back of a wooden spoon to release their juices. Add the balsamic vinegar, garlic, and remaining tablespoon of butter, then simmer until the mixture thickens. Season with salt and pepper.

Spread pesto, mozzarella, and tomato sauce onto a slice of bread. Place another slice of bread on top and coat the outside with butter. Repeat to make the second sandwich.

Place the sandwiches in a skillet over medium high heat. Cook until the cheese melts and both sides are browned, flipping once or twice as needed.