In a large pot, combine peas, ham, broth, water, bay leaf, and parsley. Add in onion, celery, carrots, thyme, pepper, and salt (if using). Bring to a boil, reduce heat to low and simmer covered for 1 ½ hours. Stir once, about half way through.
Remove bay leaf and discard. Remove ham bone and chop meat. Add meat back to soup and cook on low 15-30 minutes or until reaches your desired consistency.