Soak beans separately overnight and drain.
In a large sauce pot, place both kinds of beans, onions, zucchini, tomatoes, celery, potatoes, leeks and olive oil and cover by 1 inch with cool water. Cover pot and bring to a boil. Lower heat and simmer 1 1/2 hours until beans are tender. Add pasta, turn heat to a boil and cook until "al dente". Divide among bowls and top each bowl of minestrone with a dollop of pesto.