Rinse the ham hocks and place them in a 4- to 6-quart slow cooker along with the peas, carrots, celery, onion, garlic, broth, bay leaf, and thyme.
Cook, covered, until the meat is tender, on high for 4 to 5 hours or on low for 7 to 8 hours.
Remove and discard the bay leaf. Transfer the ham hocks to a plate and let sit until cool enough to handle, at least 10 minutes. Shred the meat and stir it into the soup.