Add 6 cups of water, split peas and rice, bring to a boil, then simmer about 30 minutes, stirring occasionally and scrapping bottom of pot as split peas tend to stick to bottom.
After split peas and rice have cooked 30 minutes, add broth, carrots, celery and spices. Cook another 30 minutes or so, adding remaining water (if needed) until split peas and rice are done.
Add salt & pepper to taste.
Notes
You can use previously cooked rice to reduce cook time.