Put the ham bone or hock in a soup pot or Dutch oven and cover it with water. Bring it to the boil, turn down the heat and simmer for at least 2 hours. Clean and chop the celery, carrots and onion into half inch pieces. Peel the potatoes and cut into inch cubes. Add these vegetables and simmer for an hour. Taste the broth and adjust the seasoning.

Remove the ham bone from the pot. Let it cool until it is easy to cut off the meat and return the meat to the pot. Wash the cabbage, removing any damaged outer leaves, and cut it into eighths. Add the cabbage to the pot about 20 minutes before serving and simmer until tender but not mushy.