Prepare the Marinade:
In a gallon-sized ziplock bag, add the minced garlic, shallot, basil, Dijon mustard, salt, pepper, balsamic vinegar, and olive oil. Close the bag and shake well to combine.

Marinate the Chicken:
Trim the chicken breasts of any excess fat and place them in the marinade bag. Massage the marinade into the chicken and refrigerate for approximately 8 hours or overnight.

Preheat the Oven:
Preheat your oven to 425°F (220°C). Remove the marinated chicken from the fridge and let it warm up on the counter for about 15-20 minutes.

Sear the Chicken:
Heat a large oven-safe skillet (preferably cast iron) over medium-high heat with a drizzle of oil. Add the chicken and caramelize each side — 3 minutes on one side, and 2 minutes on the other.

Bake the Chicken:
Turn off the burner and place the skillet in the oven. Bake for approximately 15-20 minutes (depending on the thickness of the chicken). Use a meat thermometer to ensure the internal temperature reaches 165°F (74°C).

Prepare the Toppings:
While the chicken is baking, chop the topping ingredients (cherry tomatoes, mozzarella cheese, and basil). Set them aside.

Add Cherry Tomatoes and Cheese:
For the last 7 minutes of cooking, add the cherry tomatoes around the chicken. After the chicken has cooked through, place slices of mozzarella cheese over each chicken breast and return the skillet to the oven.

Broil the Chicken:
Switch the oven setting to BROIL and broil on HIGH for several minutes until the cheese is melted to your liking.

Finish and Serve:
Once the cheese is melted, sprinkle the chicken with sliced fresh basil and drizzle with balsamic glaze if desired. Serve hot.