Preheat the oven to 400°F (200°C).
In a large skillet over medium heat, warm 1 tablespoon of olive oil and briefly sauté the sliced onions and garlic until fragrant and softened.
In a mixing bowl, combine zucchini slices, cherry tomatoes, oregano, basil, salt, pepper, and the remaining olive oil. Toss until vegetables are well coated.
Place the chicken breasts in the center of a greased baking dish. Season both sides with salt and pepper.
Spread the vegetable mixture around and partially over the chicken. Drizzle the balsamic vinegar evenly over the entire dish.
Cover the baking dish with foil and bake for 25 minutes.
Remove the foil and sprinkle mozzarella and Parmesan over the top. Bake uncovered for another 10–15 minutes until the cheese is melted and bubbly and the chicken reaches an internal temperature of 165°F (74°C).
Once done, remove from the oven and let rest for 5 minutes. Garnish with fresh basil leaves before serving.