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 the meat from the bone.
Add meat back to soup and cook on low 15-30 minutes or until reaches your desired consistency.
Notes
Refrigerate leftovers in a covered container for up to a week.
Reheat on the stovetop over low heat, or quickly in the microwave.
Freeze portions in zippered bags for up to 3 months. Thaw in the refrigerator, then reheat on low and stir in some broth if needed.