Heat oil in a large, heavy-duty pot over medium-high heat. Add onion, celery and garlic and sauté for 5 minutes, or until softened. Add water, carrots, sweet potato, parsnip, parsley, oregano, salt and pepper and bring to a boil. Reduce heat and simmer for 10 minutes, stirring occasionally. Add rice and cook for 20 minutes, stirring occasionally, until rice is tender. Add black-eyed peas and cook until thoroughly heated.
Remove from heat and let stand for 10 minutes. Serve in shallow bowls with bread, if desired.