Heat oven to 450° F. Slice a thin piece from the rounded bottom of each tomato so they sit upright. Slice each tomato in half horizontally. Arrange the tomato halves, cut-side up, on a shallow roasting pan or rimmed baking sheet lined with foil. Drizzle with the oil, then sprinkle on the salt and pepper. Scatter the garlic over the tomatoes. Roast until they're softened and warmed through, about 15 minutes. (Underripe tomatoes may take 5 to 15 minutes longer.) Meanwhile, cut the mozzarella into six 1/2-inch-thick slices. Using a spatula, sandwich each cheese slice between 2 hot tomato halves. The heat of the tomatoes will melt the cheese slightly. Drizzle with any juices that collected in the roasting pan and garnish with the basil.
Tip: To slice a soft cheese such as fresh mozzarella easily, first freeze it for 30 minutes. Bring the slices to room temperature before continuing with the recipe.