Pat the chicken breasts dry and slice each horizontally to make 4 thinner fillets.
Season both sides of the chicken fillets with Italian seasoning, minced garlic, and a pinch of salt.
Heat 1 tablespoon olive oil in a grill pan or large skillet over medium-high heat.
Sear the chicken fillets until browned and cooked through, about 5–7 minutes per side depending on thickness; remove from the pan and let rest.
While the chicken cooks, combine the chopped Roma tomatoes, finely chopped red onion (or 3 cloves minced garlic if using), shredded basil, 2 tablespoons olive oil, and a pinch of salt in a bowl; mix gently to make the bruschetta topping.
Spoon the tomato mixture evenly over each chicken fillet, then sprinkle with freshly shaved Parmesan cheese.
To make a balsamic glaze (optional), combine the 1/2 cup balsamic vinegar and 2 teaspoons brown sugar in a small saucepan and bring to a boil, then reduce heat and simmer until thickened to a glaze, about 5–8 minutes; if omitting sugar, simmer 12–15 minutes until reduced.
Drizzle the balsamic glaze over the plated chicken if desired and serve immediately.