Cook penne according to package directions. Drain and set aside.
In a large skillet, heat oil over medium-high heat. Add onion and garlic and cook 3 minutes, until soft. Add broccoli, carrots and mushrooms and cook 3 minutes, until mushrooms soften. Add chicken, red peppers, tomatoes, and broth and bring to a simmer. Stir in penne and peas cook 2 minutes to heat through and season, to taste, with salt and black pepper. Transfer mixture to a serving plate and top with Parmesan and basil.