Sort through the peas to ensure there is no debris. Rinse and drain well.
In a large pot, combine peas, ham, water, broth, parsley, and bay leaf. Bring to a boil, reduce heat to low, and simmer covered for 1 hour.
Add in celery, carrots, onion, pepper, thyme, and salt. Cover and simmer 45 minutes more.
Remove ham bone and chop the meat. Return the meat to the soup and cook uncovered until thickened and the peas have broken down and the soup has thickened, about 20 minutes more.
Discard the bay leaf and season with salt and additional pepper to taste.
