Lemon, grated cheese, and cooking water make up the remarkably simple sauce for this pasta. Baby fingerling potatoes in different colors look great, but any small boiling potatoes will taste good -- just cut them into quarters if need be.
Follow these steps when you cook the pasta for this dish: Bring a large pot of water (6 quarts) to a boil -- you want enough water so the pasta can move around. Season the water with 1/4 cup coarse salt. (The water should be well seasoned; think "salty like the sea.") Cook 1 pound of pasta until al dente. Drain, reserving at least 2 cups cooking water. The pasta releases starch as it cooks, and the starchy water is essential to the sauce.