01 - Preheat oven to 400°F. Lightly grease a 9x13-inch baking dish with olive oil or cooking spray.
02 - In a small mixing bowl, whisk together the balsamic vinegar, honey, Dijon mustard, minced garlic, olive oil, salt, and pepper until smooth and well combined.
03 - Arrange the chicken breasts in the prepared baking dish. Pour the balsamic mixture evenly over the chicken, turning each breast to coat thoroughly. Allow to rest for 10 minutes for enhanced flavor absorption.
04 - Bake uncovered for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F. Baste once with pan juices halfway through cooking to keep the meat moist.
05 - Remove the dish from the oven and scatter crumbled goat cheese evenly over each chicken breast. Return to the oven for 2 to 3 minutes, just until the cheese begins to soften and warm through.
06 - Transfer the chicken to serving plates. Spoon the pan sauce over each portion and sprinkle generously with chopped fresh basil. Finish with an extra drizzle of balsamic glaze and a crack of black pepper if desired. Serve immediately.