Heat olive oil over medium heat in a large skillet for one minute. Add onion and saute for one minute, then add garlic, zucchini, & mushrooms and continue to saute over medium heat, stirring occasionally, for about seven minutes or until mushrooms are softened.
Stir in chicken and season with oregano, crushed red pepper, and Italian seasoning.
Stir in 1.5 cups of water, tomatoes, and tomato sauce, increase heat to medium-high, and bring to a boil.
Stir in pasta and reduce heat to medium low. (The pan will be quite full at this point, but it will cook down a bit!)
Cover skillet and simmer for 20 minutes or until pasta is tender and liquid has been almost fully incorporated, stirring a couple of times to ensure all of the penne cooks evenly.
Once pasta is tender, sprinkle shredded mozzarella across the top of everything, then top with Parmesan.
Replace lid, reduce heat to low, and simmer for another 5 minutes or until cheese is nicely melted, then serve.
Since I used already-seasoned leftover Italian pulled chicken in my skillet here, I omitted Italian seasoning -- If you're using plain shredded chicken, however, you'll want to add it in, and adjust the level of your seasonings to taste. If you don't have leftover cooked chicken, you can also cook chicken breast in the skillet before adding the onion, then remove and shred it for use in the recipe.
Italian Chicken, Veggie, and Pasta Skillet from Mashup Mom: https://www.mashupmom.com/italian-chicken-veggie-and-pasta-skillet/