Peel the potatoes, cut into cubes not too big and set aside. Slice the mushrooms into thin slices. In a large pot, melt the butter and add the garlic. When it is golden, add the mushrooms and pan-fry a few minutes. Remove the garlic and then add the chopped potatoes and pasta. Stir and cook by adding one at a time some ladles of hot broth and saffron, as a risotto. Adjust salt if necessary, although it is not necessary if you use a very tasty broth. Add the chopped parsley. Once the pasta is ready, turn off the heat and stir with a few tablespoons of Parmesan cheese. Serve hot with a sprinkling of freshly ground black pepper.