In a bowl, whisk together balsamic vinegar, honey, oil, minced garlic, Italian seasoning, and Dijon mustard. Season with salt and pepper. Set aside.

In a separate bowl, toss together halved tomatoes, mozzarella balls, and chopped basil. Season with salt and pepper. Set aside.

Preheat oven to 400°F.

Slice chicken breasts in half lengthwise to create 2 to 3 thinner slices. Cover with plastic wrap and pound to 1/2 inch thick. Pat completely dry with paper towels.

Season each side of chicken with Italian seasoning, salt, and pepper.

Combine flour and Parmesan cheese on a plate. Dredge chicken pieces in the mixture and tap off excess.

Heat olive oil in large oven-safe skillet over medium-high heat. Sear chicken in batches for 4 to 5 minutes per side until a golden crust develops. Set seared chicken aside.

Add balsamic sauce mixture to the hot skillet. It should quickly come to a simmer. Use a wooden spoon to scrape up brown bits from the bottom of the pan.

Immediately remove pan from heat. Return chicken to the skillet and top with the tomato-mozzarella mixture.

Bake uncovered for 18 to 23 minutes until chicken is fully cooked (internal temperature 165°F). Remove from oven and rest 5 minutes before serving.