Bring a large pot of salted water to boil. Cook the pasta to al dente and save 1 cup of pasta water.
Add cornstarch to ¼ cup of water and heat in microwave-safe cup measurer on high heat for 1 minute. Make sure the cornstarch is completely incorporated and set aside.
Add the cheese, olive oil and cornstarch mixture to a food processor, blending until a paste forms.
Heat freshly ground pepper in large skillet over medium heat until it is fragrant, about 30 seconds. Deglaze with ½ cup of the reserved pasta water.
Add in the cheese paste, mixing until it forms a sauce. Add the pasta, tossing to coat. If the sauce is too thick, add more pasta water 1 tablespoon at a time.
Top with some freshly grated cheese and pepper and serve immediately.
Notes
Make sure the water you are cooking the pasta in is salted as some of the flavor comes from it.
Adding cornstarch to the cheese mixture helps emulsify the cheese and water, creating a smooth and creamy sauce.
DO NOT overcook the pasta when boiling. You want it just al dente or slightly under. It continues to cook with the sauce.
Toasting the black pepper enhances the flavor, but can be skipped if you want. Speaking of pepper, only use freshly ground.
Don't use pre-shredded cheese. You want if finely grated so it melts well. Pre-shredded has added ingredients that will just make it clump up.