Pasta e Patate: Pasta and Potato Soup

Name: Pasta e Patate: Pasta and Potato Soup
Ingredients: 1/4 cup/50 ml extra-virgin olive oil, plus extra for drizzling; 4 ounces/100 g prosciutto or salami, chopped; 1 white onion, chopped; 1 celery, coarsely chopped; 1 carrot, coarsely chopped; 1 fresh chile pepper, chopped; Salt and freshly ground black pepper; 2 potatoes, peeled and cubed; 2 1/2 cups/600 ml water; 10 ounces/300 g tomato puree; 10 ounces/300 g spaghetti, broken into small pieces; 1/2 cup/125 ml Pecorino cheese, chopped; 1/2 cup/125 ml freshly grated cheese Parmigiano