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In a large soup pot over medium heat, add the salt pork and render with the butter.
Turn heat up to medium high, add leek, carrots, onion, zucchini, and celery. Sauté until tender, about 5 minutes.
Add the chicken stock, potato, tomatoes, bay leaf, basil, parsley, and water. Turn heat to medium low and simmer for 30 minutes.
Add the beans and rice. Simmer for 15 minutes.
Add the green peas. Simmer for 15 minutes more. Add salt and pepper to taste before serving.