In a large Dutch oven or deep skillet, add the chicken, garlic, Italian seasoning, salt, black pepper, hot sauce, chicken broth, milk, Alfredo sauce, and uncooked pasta. Stir well to combine. Bring to a gentle boil over medium-high heat.
Reduce heat to medium-low and cover. Cook for 15 to 20 minutes, stirring every few minutes to prevent sticking, until the pasta is tender and the chicken is cooked through.
Stir in the frozen mixed vegetables and cook for 2 to 3 minutes, or until heated through. Remove from heat and stir in the mozzarella cheese and Parmesan cheese until melted and creamy.
Let the pasta rest for 3 to 5 minutes to allow the sauce to thicken. Garnish with fresh parsley and additional Parmesan cheese if desired. Serve hot with garlic bread or a simple side salad.