In a 4-quart Dutch oven, cook ground beef and shredded carrot over medium heat until meat is brown. Drain off fat. Stir tomato soup, the water, uncooked ziti, dried basil (if using), onion powder, and garlic powder into meat mixture in Dutch oven.
Bring mixture to boiling; reduce heat. Cover and cook about 25 minutes or until ziti is tender, stirring occasionally. Stir in fresh basil (if using) and mozzarella cheese. Sprinkle individual servings with Parmesan cheese.