Place ham in the bottom of the slow-cooker. Add the beans, carrots, celery, onion,garlic, salt, and water. Cook on high for 4-6 hours or low for 6-8 hours until beans are tender.
Discard garlic clove. Remove ham, separate meat from bone, and shred or cut into bite size pieces and add back to soup.
Serve in bowls topped with fresh parsley and a side of fresh bread or rolls.