In a stock pot, submerge the hambone, celery stalk, whole carrot and half onion in the water. Boil for 30-45 minutes or until the meat begins to easily fall off the hambone. Remove the hambone and vegetables from the broth. Discard veggies and shred the meat from the bone and set aside.
Stir in the beef base, chili powder and salt and pepper to the ham broth and bring to a simmer. Add the diced onion, shredded carrot, bell pepper, cabbage and potatoes and simmer until the cabbage is tender and the potatoes are cooked through. Stir the shredded ham back into the soup to reheat. Serve and enjoy!