Here is a cabbage soup recipe I just stole off Allrecipes.com. Sounds pretty good and would be great with your ham tossed into the mix. I may give this a try myself.
Place carrots, onions, tomatoes, cabbage, green beans, peppers, and celery in a large pot. Add onion soup mix, tomato juice, beef broth, and enough water to cover vegetables. Simmer until vegetables are tender. May be stored in the refrigerator for several days.