In a medium bowl, stir together the diced tomatoes, minced garlic, chopped basil, balsamic vinegar, balsamic glaze, and 1 tablespoon olive oil.
Add 1/4 teaspoon salt and a few turns of black pepper.
Let the tomato mixture sit while you cook everything else.
Bring a large pot of salted water to a boil.
Cook the penne until al dente, following the package directions.
Reserve 1/2 cup pasta water, then drain the pasta.
Meanwhile, slice the chicken breasts in half lengthwise for thinner cutlets.
Season both sides with the remaining salt, pepper, and Italian seasoning.
Heat 1 tablespoon olive oil in a large skillet over medium heat.
Cook the chicken for 4 to 5 minutes per side, until golden and cooked through.
Let the chicken rest for 5 minutes.
Slice the chicken.
Return the drained pasta to the warm pot.
Toss in half the tomato mixture.
Pour in a splash of the reserved pasta water if needed.
Top with the mozzarella and Parmesan.
Stir lightly until the cheese softens.
Add the sliced chicken.
Spoon the remaining tomato mixture over the top.
Finish with more basil and a drizzle of balsamic glaze, if wanted.