Heat the olive oil in a large pot with a lid, add the onion, carrot and celery. Cook very slowly for 15 minutes with the lid on, stirring occasionally. Do not brown the vegetables. Add the rest of the vegetables, the basil, and lightly season with salt and pepper. Add enough water to cover the ingredients in the pot. Simmer until the vegetables are tender, about one half hour. Add the pasta and continue to cook until it is tender, but not too soft. Remove from heat, check the seasonings. Meanwhile make the pistou.
In a mortar, crush the garlic with pepper and some salt. Be careful to use just a small amount of salt because the Parmesan is salty. Add the pine nuts then the basil, crushing and mashing until the mixture becomes a pulp. Add the Parmesan, then whisk in olive oil gradually, to reach the consistency of mayonnaise. Adjust the seasonings.
If you wish to make the pistou in a food processor, blend the basil, garlic, pine nuts and Parmesan until the mixture is finely chopped. With the motor running, drizzle in the olive oil to until the mixture becomes the consistence of mayonnaise. Season with salt and pepper to taste.
Serve the soup hot in bowls, and pass the pistou for people to help themselves. I like a rustic bread with this soup, and an Italian red wine, which can stand up to the power of the pistou.