Preheat the oven to 425°F (220°C) and lightly grease a 9x13-inch casserole dish. Place the chicken breasts on a cutting board and cover them with plastic wrap. Using a rolling pin, meat mallet, or small skillet, gently pound the thicker end of each chicken breast to create an even thickness, which helps ensure uniform cooking. Arrange the chicken breasts in a single layer in the prepared baking dish. In a small bowl, whisk together the chicken broth, balsamic vinegar, olive oil, basil pesto, honey, cornstarch, minced garlic, salt, and black pepper until well combined. Pour the balsamic mixture evenly over the chicken. Scatter the cherry tomatoes around the chicken in the dish. Bake for 15 to 23 minutes, depending on the thickness of the chicken breasts, or until the internal temperature reaches at least 165°F (74°C). Remove the dish from the oven and place a slice of mozzarella cheese on top of each chicken breast. Return to the oven and broil for 1 to 2 minutes, just until the cheese is melted and bubbly. Finish by sprinkling with freshly chopped basil and serve immediately.