First, peel and thinly slice the carrots. Peel the potatoes and cut them into a 1/2-inch dice. In a large saucepan place the broth, carrots, and potatoes. Bring to a boil over medium heat, and then reduce heat to low, cover, and simmer until the potatoes are tender, about 10 minutes. Then add the beans, spinach, and pasta to the soup. Bring the soup back to a boil, cover and simmer over medium heat until the pasta is cooked, about 10 minutes. Season to taste with salt and pepper, and remove from heat. Add the cheese, stirring until it is softened. Ladle into bowls and serve immediately.