Rinse, drain and sort peas.
Place oil in a large pot over medium heat. Add carrots, celery and onion. Saute until soft.
Add peas, water and ham to pot. Bring to a boil, lower heat and simmer until peas have become "mush" and liquid is mostly absorbed, about 1 hour. Stir occasionally.
If you used a ham shank, remove it, discard bone, and cut up the meat and add it back to the soup.
You can add safe chicken or beef bouillon to taste.
You can omit any of the vegetables.