Trim the roots and dark green ends from the leeks. Split leeks lengthwise, then rinse in a bowl of water (or under the faucet) to release any dirt. Cut the leeks, carrots, and celery into 1/2-inch dice. Mince the garlic.

Heat the olive oil in a large frying pan over medium heat. Add the leeks, carrots, and celery and cook, stirring, until softened, about 6 minutes. Add the garlic and cook until fragrant, about 2 minutes.

Rinse the beans in a fine strainer, and pick through to remove any stones. Add beans to a 6 to 8 qt. slow cooker along with the vegetables, bay leaf, salt, pepper, thyme, chicken broth, water, and ham hock. Stir to combine.

Cover the slow cooker and cook on high until beans are tender, and ham falls from the bone when tested with a fork, 7-8 hours.

Remove the ham hock and transfer to a cutting board. Discard any bones, fat, skin, and gristle. Cut meat into bite-size pieces and return to the soup.

Chop the parsley. Taste the soup and add more salt and pepper if desired. Discard bay leaf. Ladle soup into bowls, top with parsley, and serve.