Preheat oven to 350F.
In a mixing bowl, combine tomatoes, 1/2 cup cheese and basil; stir just until combined and set aside.
Pound each chicken breast to 1/4-inch thickness, being careful not to tear or rip through.
Season chicken with salt and pepper.
Spoon previously prepared tomato mixture over each chicken breast. You don't have to use all the stuffing - any leftovers can be spooned over chicken right before baking.
Roll up the chicken breasts, wrapping them tightly, and secure ends with toothpicks.
Heat extra virgin olive oil in a stovetop and oven safe large skillet.
Add prepared chicken breasts to hot oil and cook over medium-high heat for about 6 minutes, or until lightly browned on all sides.
In the meantime, prepare the Balsamic sauce. In a medium bowl combine balsamic vinegar, chicken broth, garlic, and Italian seasoning; whisk until thoroughly combined.
Remove chicken from heat.
If you have some extra tomato mixture, spoon it over the chicken.
Pour prepared balsamic sauce over chicken.
Transfer to oven and bake for 20 minutes; remove from oven, flip the chicken over, and return to oven for 15 more minutes.
Sprinkle with remaining mozzarella cheese and continue to bake for 5 more minutes.
Remove from heat and let stand for a few minutes.
Serve with pasta, rice, vegetables, or a fresh salad.