My husband and I actually collaborated on this recipe! We always make it with the left over Christmas ham. Even if you don't like peas, this is wonderful. Our son, Nick, who doesn't like peas will even eat this soup. Yum!
Rinse the split peas under cold running water. Discard any discolored peas. Place the peas in a large kettle and add water to cover. Bring to a boil and boil 2 minutes. Remove from the heat and let soak 1 hour. Drain. (Or you can just soak the peas overnight, covered)
Put the peas back in the kettle and add the measured water (or chicken broth), ham bone or hock, onion, leeks, celery, parsley, salt, peppercorns and bay leaves. Bring to a boil. Reduce the heat, cover and simmer gently until the peas are tender, 1 to 1 1/2 hours. Skim occasionally.
Remove the bay leaves and the ham bone or hock from the soup. Cut the meat off the bone, discarding any fat, and chop the meat finely. Set aside. Discard the ham bone and the bay leaves.
Puree the soup in batches in a food processor or blender. You can also use a hand blender. Pour into a clean saucepan and add the chopped ham. Check the seasoning. Add the frozen peas and simmer the soup 3 to 4 minutes to heat through before serving.