Add chicken into a shallow bowl and stir in the seasonings, garlic, sea salt and pepper to your taste, and 1 tablespoon olive oil. Toss until really well coated on all sides pressing seasonings into the chicken a bit, then cover and refrigerate for at least 30 minutes up to 2 hours.
Preheat your oven to 400°F.
Remove your seasoned chicken from the refrigerator 10-15 minutes prior to cooking.
Heat a large cast iron, or oven safe skillet over medium-high heat and add the remaining oil. Sear the chicken for 3 minutes on each side to give it a nice color, then add in your cherry tomatoes, and drizzle everything with balsamic vinegar.
Place this entire skillet into your preheated 400° oven and bake uncovered until cooked through and no longer pink in the inside, about 10-12 minutes. Sprinkle chicken with shredded mozzarella, then return to the oven and continue to bake for just a minute until cheese is nice and melted.
Garnish with fresh basil.