1. Pulse onion, carrot, celery, and garlic in a food processor or until finely chopped.
2. In a large saucepan, heat oil over medium heat. Add chopped vegetables and cook, stirring occasionally, about 6 minutes. Stir in peas, ham hock, broth, water, salt, pepper, and bay leaf. Bring to a boil. reduce heat to medium-low and simmer, partially covered, until the peas fall apart and thicken the soup, about 2 hours.
3. Remove the ham hock and bay leaf. When ham is cool, pull the meat from the bone and shred it into bite-size pieces. Puree the soup in batches in food processor, then return it to the saucepan. Stir in the rice and ham. Makes 11-1/2 cups.