This recipe is the classic way to make this dish. Achingly simple and much lighter than the Italian-American counterpart, try this for yourself if you're looking for a comforting Italian classic in a flash.
Bring a large pot of heavily salted water to a rolling boil. Add the pasta, stir to ensure it doesn't stick together, and cook for one minute less than the package suggests.
Meanwhile, melt the butter in a large skillet over medium heat. While the pasta is cooking, ladle about 125 ml (1/2 cup) of the pasta cooking water into the pan. Whisking constantly, gradually sprinkle in the cheese until a loose yet homogenous sauce has formed.
Using tongs, remove the pasta from the cooking water (do not drain the water!) and transfer it directly to the skillet.
Toss the pasta in the sauce, adding a bit more pasta water if needed to loosen the consistency, until the sauce coats the noodles and it is glossy and emulsified, about one minute. Serve immediately, topping with more Parmigiano Reggiano cheese and black pepper to taste.