Add 2 quarts of water and 2 tablespoons of salt to a large pot. Set pot over medium-high heat and bring water to a boil. Drop spaghetti into water and cook until al dente, 2–3 minutes. Set aside 1 cup of pasta water and drain the pasta.

Transfer pasta to a warm serving bowl. Sprinkle all of the cheese and most of the pepper over the pasta.

Toss vigorously, adding pasta water 1 tablespoonful at a time. The water will melt the cheese to create a smooth, creamy sauce. Garnish with remaining pepper and serve hot.