Arrange tomatoes, cut sides up, on a baking sheet. Drizzle with 1/4 cup olive oil and 1 1/2 tablespoon balsamic vinegar and sprinkle with garlic, sugar, sea salt, and black pepper.
Roast tomatoes in the preheated oven until they begin to turn brown and the juices become thick and sticky, about 2 hours. Let tomatoes cool to room temperature.
Place tomato halves and slices of mozzarella cheese onto a serving platter, alternating tomatoes and cheese to make an attractive pattern; sprinkle salad with basil. Drizzle with 1 tablespoon extra-virgin olive oil and 1 1/2 teaspoon balsamic vinegar.