Place half of sausage in an electric slow cooker; top with sauerkraut, remaining sausage, apple slices, and onion rings. Pour broth over mixture, and sprinkle with caraway seeds. Cover with lid, and cook on high-heat setting for 4 hours or until apples and onion are tender.
Place potatoes in a saucepan; cover with water, and bring to a boil. Cook 20 minutes or until tender; drain.
Arrange sausage mixture and potatoes on individual plates, and sprinkle cheese over sausage mixture.