Place the garbanzo beans into a large container and cover with several inches of cool water; let stand 8 hours to overnight.
The next day, rinse the soaked beans and place them into a slow cooker; place the ham bone in the cooker, and pour in enough water to cover the beans and ham bone by several inches. Set the cooker to Low, and cook for 8 hours.
Skim any foam from the top of the soup, and remove the ham bone. Strip as much meat as possible from the ham bone, and return the meat to the slow cooker; discard the bone. Stir in potatoes, carrots, frozen corn, and black pepper to taste. Set the cooker on Low, and cook for 1 hour; then turn the heat up to High and cook 1 more hour (10 hours total cooking time).
