In a large bowl or resealable bag, combine 2 tablespoons olive oil, 1 tablespoon balsamic vinegar, 2 teaspoons garlic powder, 1 teaspoon Italian seasoning, and optional 1 teaspoon red pepper flakes. Add the chicken, coat well, and refrigerate to marinate at least 30 minutes or up to overnight.
Preheat the oven to 425°F (220°C).
In a 9x13 baking dish, pour 2 tablespoons olive oil. In a bowl, toss 24 oz cherry tomatoes with 2 tablespoons balsamic vinegar, 2 tablespoons chopped fresh basil, 1 tablespoon honey, 1 teaspoon garlic powder, and 1 teaspoon fresh thyme leaves until combined; spread the tomato mixture evenly in the dish.
Arrange the marinated chicken breasts over the bed of tomatoes in a single layer.
Sprinkle 2 cups shredded mozzarella over the chicken, season with salt and pepper to taste, and tuck 4–5 fresh thyme sprigs on top.
Bake for 35–38 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and is cooked through.
Remove from the oven, discard thyme sprigs if desired, and sprinkle 2–3 tablespoons chopped fresh basil over the chicken before serving.