To make the pesto: In a large stone mortar, place the pine nuts, basil, garlic, and salt, and grind with a pestle until paste. Drizzle in the olive oil, beating with a wooden spoon. This can also be done in a food processor. Store in jars, topped with extra-virgin olive oil, for up to 1 week.
To make the minestrone:
Soak the borlotti and Cannelloni beans separately overnight and drain.
In a large soup pot, place both kinds of beans, the onion, zucchini, tomatoes, celery, potatoes, leeks, and olive oil, and cover by 1-inch with cool water. Cover the pot and bring to a boil. Lower the heat and simmer until the beans are tender about 1 hour to 1 hour and 30 minutes. Add the pasta, and turn the heat to high. Cook the pasta at a boil until al dente. Divide the soup among 4 bowls and top each bowl of minestrone with a dollop of pesto floating on top.