Drain the beans & combine with the water in a Dutch oven. Bring to a boil & cok at a high heat for 10 minutes. Reduce heat & simmer, covered, for another 5 minutes.
Add the potatoes, squash, zucchini, tomato & mushrooms & cook over medium heat, stirring from time to time. After about 15 minutes, add the carrot, celery, garlic & onion. Simmer for another 15 minutes, stirring occasionally. Add the olive oil & salt. Continue simmering, pressing the beans & potatoes against the side of the pot to make the soup dense. After another 15 minutes cooking, add the pasta & simmer for 9 or 10 minutes until it is al dente. Just as the heat is turned off, stir in the pesto. Let the soup cool until it is tepid & serve it with drizzles of olive oil on top.