Fill a large stockpot about 2/3 with generously-salted water. Bring to the boil, and add your pasta, cooking until only just al dente. (You can grate your cheese while you wait for the water to boil!).
Right before your pasta finishes boiling, carefully scoop out about 2 cups worth of starchy water and reserve.
Drain the pasta using a colander. Transfer the pasta back to the stockpot (take off the heat).
Add the butter, olive oil, and 1 cup of the starchy water, and quickly toss to combine. Next, add the grated cheese, black pepper, and toss again. Keep adding the remainder of the starchy water until all of the cheese has melted and a silky sauce starts to form.
Serve immediately, garnished with fresh parsley.