In a medium saucepan over high heat, combine the broth, potatoes, onions, carrots and celery. Bring to a boil and reduce heat to low. Cover and simmer about 15 minutes, or until potatoes are tender. Mash lightly with a potato masher.
Add American cheese, milk and hot sauce and continue cooking over low heat until cheese melts, stirring occasionally. Add salt and pepper to taste. Garnish with fresh parsley and hot pepper sauce, if desired.