Stir broth, tomatoes, brown sugar, vinegar, Italian seasoning blend, salt, and pepper in the insert of a 6-qt. slow cooker. Stir in onion and garlic and cover. Set the slow cooker to low heat for 4 hours. In the last half hour of cooking stir in the ziti, cover and continue cooking until the timer goes off.
Stir the basil into the soup and break up any ziti that is stuck together. Divide between 4 bowls and top with cheese and parsley.
