Season the chicken chunks with salt and freshly ground black pepper, then set aside.
Heat the olive oil in a wide 12-inch skillet over medium heat. Add the chopped onion and cook, stirring often, until softened, about 3 minutes.
Add the chicken in a single layer and brown on both sides, about 5 to 7 minutes total. Stir as needed so the pieces sear evenly.
Stir in the minced garlic and cook for 1 minute, just until fragrant.
Add the uncooked penne pasta, chicken broth, water, broccoli, red bell pepper, carrots, and frozen peas. Stir well, scraping up any browned bits from the bottom of the pan.
Bring the mixture to a boil over medium-high heat. Once boiling, reduce the heat to low, cover, and simmer for 22 minutes, or until the pasta and vegetables are tender.
Uncover and continue cooking for about 5 minutes, stirring occasionally, until most of the liquid has absorbed and the pasta is cooked through.
Remove the skillet from the heat. Stir in the cream cheese, shredded mozzarella, and grated Parmesan until melted into a smooth, creamy sauce.
Taste and season with additional salt and black pepper as needed. Divide into four bowls and garnish with chopped fresh Italian parsley if desired. Serve hot.