Step 1To make the pistou in a food processor, turn on a processor and drop in the garlic. Scrape down the sides of the work bowl, add the basil and salt to taste (1/4 to 1/2 teaspoon) and process until finely chopped. Scrape down the sides once more and turn on the machine. Drizzle in the oil with the machine running, then drop in the tomato if using. Process to a paste. Taste and add more salt, if necessary. Stir in the Parmesan. To make the pistou in a mortar and pestle, pound the garlic with the salt to a paste. Add the basil, a handful at a time, and pound and grind the basil to a paste. Add the optional tomato and work to a paste with the basil. Drop by drop, work in the olive oil. Stir in the cheese.
Step 1Combine the drained white beans and 2 quarts water, and bring to a boil. Skim off any foam, then add the onion, 2 garlic cloves and the bouquet garni. Bring to a boil, reduce the heat, cover and simmer 1 hour.
Step 2Add the remaining 2 quarts water, the remaining garlic, half the green beans, half the zucchini, the cranberry beans, carrots, celery, leeks, turnips, potatoes and tomatoes and their liquid to the pot and bring to a boil. Add salt to taste (be generous), reduce the heat, cover and simmer 1 hour. Taste and adjust the seasonings.
Step 3While the soup is simmering, blanch or steam the remaining green beans and zucchini until tender but bright, about 5 to 8 minutes, and set aside.
Step 4Add the pasta to the soup about 10 minutes before serving and simmer until cooked al dente. Add pepper, and taste and adjust the salt. Stir the blanched or steamed green vegetables into the soup and heat through.
Step 5To serve, either stir the Pistou into the pot, place a dollop on each bowl and stir in or pass the Pistou in a bowl and let people stir in their own. Pass additional Parmesan or Gruyere for sprinkling.