Whisk together the balsamic vinegar and 1/2 tablespoon olive oil in a small bowl to make the dressing.
Add chopped tomato to the dressing and season with salt and pepper. Thoroughly combine and set aside.
Pound chicken until very thin. Dry with paper towels and season with salt and pepper. Place each chicken breast on a large piece of plastic wrap.
On each breast, arrange 2 basil leaves, slices of mozzarella, and top with chopped tomatoes, using a slotted spoon to transfer them as to leave behind the excess dressing.
Roll the chicken very tightly, using the plastic wrap as a guide. When you are finished, the chicken should be very tightly rolled and completely covered in plastic wrap.
Place chicken rolls in refrigerator for 30 minutes to set. Meanwhile preheat oven to 350°F and prepare panko.
Heat the remaining 1/2 tablespoon of oil over medium-high heat in a small skillet. Toast the panko until golden, about 7 minutes.
Transfer panko to a shallow dish to cool. In a bowl, combine flour and cayenne (if using) with salt and pepper. Pour buttermilk into a second bowl.
Once panko bread crumbs have cooled, stir in the grated garlic and Parmesan cheese. Combine well. Line a baking dish with aluminum foil lightly greased with olive oil or cooking spray.
After 30 minutes has elapsed, remove chicken rolls from fridge. Unwrap and dip into flour mixture to coat. Tap off excess. Dip roll into buttermilk, then into panko, making sure to press the panko on if it's not sticking. Place roll into baking dish and repeat with second roll.
Bake uncovered for 40 minutes, or until chicken is no longer pink.