In a large slow cooker, combine the ham hocks, beans, broth, celery, carrots, onion, garlic and thyme sprigs. Cover and cook on low until the beans are tender, about 5 hours.
Discard the thyme stems. Using tongs, remove the ham hocks and shred the meaty parts; discard the skin, fat and bones. Using the back of a spoon, mash the garlic halves against the side of the slow cooker to squeeze the soft cloves out and stir into the soup; discard the skins. Return the shredded ham back to the slow cooker and season with salt and pepper. Ladle the soup into bowls, garnish with the thyme leaves and serve with the bread.