Preheat oven to 400°F (200°C) and line a large baking sheet with parchment paper or foil.
In a shallow bowl, mix Parmesan, panko, Italian seasoning, garlic powder, onion powder, salt, and pepper.
Pat chicken dry and brush both sides with 1 tablespoon olive oil. Dredge each piece in the Parmesan mixture and place on one side of the baking sheet.
Toss broccoli, carrots, and onion with the remaining olive oil, red pepper flakes (if using), salt, and pepper. Spread veggies on the other side of the pan.
Bake for 25–30 minutes or until the chicken is cooked through (internal temp of 165°F) and veggies are tender and golden.
Optional: Broil for an additional 2–3 minutes to crisp up the topping.