Make the soup: In a large, heavy-bottomed 6-quart stock pot, combine the olive oil and the diced onion. Stir so that the onions are coated with the oil and cook over moderate heat until soft, about 2 minutes. Add the leeks and cook for two more minutes. Add carrots, zucchini, tomato, tomato paste, cut beans, 3 quarts of cold water and salt and pepper to taste. Simmer gently for about 30 minutes. Add potatoes, green beans and pasta and cook for about 15 minutes or until potatoes are tender.

Make the Pistou in a food processor: Rinse the basil leaves and pat dry on a clean towel. Place the garlic, salt, pepper and basil in the bowl of a food processor or blender and process to a paste. Mix in the Parmesan quickly. Slowly add the oil through the funnel of the lid and process again. Taste and rectify the seasoning if desired.

Serve the soup: In a soup plate place a generous tablespoon of Pistou and serve the soup over it.