In a large saucepan over medium-high heat, warm 1tablespoon of the oil. Working in batches, sauté the beef in the oil until browned, about 4 minutes. Transfer to a plate. Add the remaining 1tablespoon oil to the pan and reduce the heat to medium. Add the onion, carrots, and celery, cover, and cook, stirring occasionally, until the onion is softened, about 5 minutes. Return the beef and any juices from the plate to the pan.
Simmer the soup
Add 6cups (48fl oz/1.5l) water to the pan and bring to a boil over high heat. Reduce the heat to medium-low and simmer, partially covered, for 1 hour. Add the potatoes, tomatoes, and green beans, and stir well. Simmer until the beef and potatoes are tender, about 20 minutes. Stir in the parsley and season to taste with salt and pepper. Ladle into bowls and serve.