Preheat the oven to 275 degrees.
12 plum tomatoes, halved lengthwise, seeds (not cores) removed
¼ cup olive oil, plus more for drizzling
1½-2 tablespoons balsamic vinegar
2 large garlic cloves, minced
2 teaspoons sugar
Kosher salt and freshly ground black pepper
16 ounces fresh salted mozzarella
12 fresh basil leaves
Arrange the tomatoes on a sheet pan, cut sides up, in a single layer. Drizzle with the olive oil and balsamic vinegar. Sprinkle with the garlic, sugar, 1½ teaspoons salt, and ½ 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. 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. If desired, sprinkle lightly with salt and pepper and drizzle lightly with olive oil. Serve at room temperature.