Arrange the tomatoes on a sheet pan, cut sides up, in a single layer. Drizzle with 1/4 cup of olive oil and the balsamic vinegar. Sprinkle with the garlic sugar, 1.5 teaspoons salt, and 0.5 teaspoon pepper. Roast for 2 hours until the tomatoes are concentrated and begin to caramelize. Allow the tomatoes to cool to room temperature.
Cut the mozzarella into slices slightly less than 1/2" thick. If the slices of mozzarella are larger than the tomatoes, cut the mozzarella slices in half. Layer the tomatoes alternately with the mozzarella on a platter and scatter the basil on top. Sprinkle lightly with salt and pepper and drizzle lightly with olive oil. Serve at room temperature.