6ouncestubetti or another small pasta suitable for soup
Peel and finely chop the onion. Peel the carrot and celery and cut into ¼-inch dice (you should get about ⅓ cup of each). Peel the potatoes, cut them into ½-inch cubes, and put them in a bowl of cold water to prevent them from discoloring. peel the tomatoes, then coarsely chop.
Put the onion, carrot, celery, and olive oil in a soup pot and place over medium-high heat. Sauté, stirring occasionally, until the vegetables begin to brown, about 10 minutes.
While the vegetables are sautéing, chop the prosciutto. When the vegetables begin to brown, add the prosciutto and cook until it loses its raw pink color.
Add the wine, bring to a boil, and cook for about 30 seconds to let the alcohol evaporate. Add the tomatoes and drained potatoes and season lightly with salt and pepper. Add the broth, cover the pot, and bring to a boil. Adjust the heat so that the broth simmers and cook for 45 minutes.
Coarsely chop the basil and add it to the soup. Add the pasta and cook until it is done.
While the pasta is cooking, grate the smoked mozzarella. Serve the soup hot with some grated cheese sprinkled on top of each serving.
You can make this soup through step 4 up to 2 days ahead. Store, covered, in the refrigerator. Reheat the soup before proceeding.