Caprese Stuffed Eggplant

Name: Caprese-Stuffed Eggplant
Ingredients: 1 eggplant (1 pound); 3 tablespoons extra-virgin olive oil, divided; ½ teaspoon salt, divided; ½ teaspoon ground pepper, divided; 8 ounces grape tomatoes, halved; 2 ½ ounces fresh mozzarella, diced; 2 tablespoons best-quality balsamic vinegar, divided; Thinly sliced basil leaves for garnish