Place the beans, leeks, carrots, celery, and potatoes in a large saucepan and cover with 7 cups water. Bring to a boil and then simmer, stirring occasionally, for 30 minutes. Add the zucchini and 3 of the tomatoes and simmer for another 20 minutes.
Meanwhile, pound the garlic and basil in a mortar and pestle or process in a food processor until pasty. Add the remaining tomato and combine until smooth. Slowly add the oil until very well combined and smooth. Season with salt and pepper.
Just before serving, add the pasta to the soup and cook until al dente, about 7 minutes. Stir 1 tablespoon of the pistou into the soup and then season with salt and pepper. Serve immediately with the Parmesan and remaining pistou.
