Add the potatoes, cabbage, onion, carrots, celery, leftover ham, bay leaves, salt, pepper, and chicken broth (everything except the parsley) to the crock of a large slow cooker.
Stir well and cook for 4-5 hours on high or 7-8 hours on low.
When the cook timer is done, stir in some chopped parsley. Remove the bay leaves and discard. Serve with cornbread, if desired.