To prepare the spice rub. In a small bowl combine brown sugar, lime juice, olive oil, paprika, chili powder, cumin, salt, and pepper.
Rub the mixture all over each side of the chicken breasts. Place into a large sealable plastic bag or container. Place into the refrigerator and marinate for 1 hour.
To make the bruschetta in a medium bowl add the Roma tomatoes. Add garlic, basil, balsamic vinegar, olive oil, salt, and pepper.
Lightly toss all of the ingredients together. Cover and refrigerate until needed.
To prepare the glaze- in a small bowl whisk together ketchup, ¼ cup balsamic vinegar, oregano and 4 tablespoons brown sugar.
Lightly grease the grates of an outdoor grill. Heat the grill to medium-high heat. Add the marinated chicken breasts to the grill.
Grill the chicken breasts turning once until they are almost fully cooked (about 10 minutes per side). Brush the chicken breasts on each side a couple of times with the glaze.
Continue to cook the chicken until it is fully cooked (the internal temperature has reached 165 degrees F.). During the last few minutes of cooking, top the chicken breasts with some mozzarella and parmesan cheese. Close the grill and cook until the cheese has melted.
Remove the chicken from the grill. Top each chicken breasts with bruschetta for serving.