Heat the oil in a large saucepan over medium heat. Add the onions, carrots, and celery, and cook until soft, about 5 minutes.
Add the potatoes, 4 cups of broth and tomatoes. Bring to a boil over high heat, reduce heat to medium-low, and simmer until potatoes are tender, 25 to 30 minutes. Add additional broth if the soup is too thick.
Stir in the beans, pasta, and zucchini (if using), and simmer until pasta is tender, 8 to 9 minutes. Stir in the pesto.
Tip: This soup tastes fabulous with freshly made croutons. To make them, remove the crust from a Panera Bread Focaccia with Asiago Cheese and cut it into 1/2-inch cubes. Heat 1/4-inch of oil in a 10-inch pan to 325ºF. Add cubes to pan, stir to coat, and then cook undisturbed until light golden brown, 2 minutes. Transfer to a towel-lined plate and sprinkle with salt.