Heat oven to 450° F. Slice a thin piece from the bottom of each tomato so the tomatoes sit upright. Slice each in half horizontally.
Arrange the tomato halves, cut-side up, on a foil-lined shallow roasting pan or rimmed baking sheet.
Drizzle the tomatoes with the oil. Season with 1 teaspoon salt and ¼ teaspoon pepper. Scatter the garlic over the tomatoes.
Roast until softened and warmed through, about 15 minutes. (Underripe tomatoes may take 5 to 15 minutes longer.)
Meanwhile, cut the mozzarella into six ½-inch-thick slices. Using a spatula, sandwich each slice between 2 hot tomato halves. (The heat will melt the cheese slightly.)
Drizzle the tomatoes with any juices that collected in the roasting pan and serve with the basil.