In a Dutch oven, combine sausage, potatoes, onion, carrots, celery, salt and pepper. Add 2-3 cups water (I sometimes use chicken broth). Bring to a boil and reduce heat. Cover and simmer for 20 minutes or until potatoes are nearly tender.
Stir in cabbage and cook for 10 minutes longer or until vegetables are tender. Stir in 2 1/2 cups milk.
Stir flour and remaining milk together and then add to soup. Cook on low until thick and bubbly. Stir in cheese until melted. Garnish with fresh parsley.