In the basin of a slow cooker, combine the beans, onion, celery, carrot, garlic, bay leaf and ham hock or bone. Pour just enough chicken broth or water over the beans to cover them. Cook on HIGH for 6-7 hours, or LOW for 8-9 hours until beans are soft and beginning to fall apart.
Thirty minutes before the beans are done cooking, remove the ham hock or bone, strip off any meat, chop and return to the slow cooker. Discard the bone. Stir in Italian seasoning, salt, pepper, and remaining chopped ham. Serve sprinkled with green onions.