Heat a medium soup pot over medium high heat. Add extra-virgin olive oil, 2 turns of the pan. Add onion, potato and zucchini and season with salt and pepper. Cook 5 or 6 minutes alone, stirring frequently, then add the canned beans and the chicken stock. Cover the pot and bring the soup up to a boil.
Preheat a panini grill or a heavy bottomed pan over medium heat. Build 4 panini: spread roll or bread with a couple ounces of cheese, then top with a few leaves of arugula and 2 slices of prosciutto for each sandwich. Place panini in sandwich press or onto hot, heavy bottomed pan. Top with another heavy skillet or a brick wrapped in foil to press sandwiches. Press sandwiches until crisp on both sides, 2 to 3 minutes on each side.
When the soup is at a boil, remove the lid. Stir in the noodles and green beans and reduce heat to low. Simmer soup an additional 5 to 6 minutes then remove it from the heat.
Combine basil, garlic, nuts and cheese in the food processor and turn it on. Stream in the extra-virgin olive oil and process until pesto is nearly smooth.
Scrape the pesto into a small bowl. Add a ladle of the soup broth to thin the pesto, then add the pesto to the soup. Stir to combine and serve soup immediately with panini, for dipping.
Recipe courtesy of Rachael Ray