In a large bowl, combine the balsamic vinegar, honey, Italian seasonings, mustard, garlic, olive oil, salt, and pepper. Whisk to combine. Add the chicken breasts and toss to coat in the marinade. Allow to marinate for 30 minutes.
Clean and oil the grill or grill pan. Heat to medium high. Grill chicken until internal temperature reaches 160ºF and no pink juices remain, about 5 minutes per side.
Top with mozzarella and cover to melt, about 2 minutes. Transfer to a plate. Top with avocado, basil, and drizzle with balsamic reduction. Serve.