Preheat oven to 400°F; line a baking sheet with parchment.
With a sharp knife, carefully cut each breast horizontally, leaving one edge intact; open like a book.
Season inside and outside with garlic powder, salt, and pepper.
Fill with mozzarella, tomatoes, and basil; fold closed and secure with toothpicks if needed.
Heat oil in an oven-safe skillet over medium-high; sear chicken 2-3 minutes per side until golden.
Transfer skillet to oven; bake 12-15 minutes until chicken reaches 165°F internally.
Remove from oven; drizzle with balsamic glaze and rest 5 minutes before serving.