Prepare all the ingredients: grate the cheese on the microplane zester (it's the best) or on the smallest holes of a box grater, grind the pepper. Set aside.
Toast the pepper: Heat the olive oil and butter in a big frying pan over low heat. When the oil and butter are hot, add the pepper. Cook, stirring, for about a minute or until the pepper is fragrant. Take the pan off the heat.
Cook the pasta: In a medium pot bring water to the boil. Water should be well-salted, don't add any oil to the water, use the smallest amount of water that will cover the pasta. Cook the pasta about 1-2 minutes less than it says on the package.
Reserve the pasta cooking water: About 3 minutes before the end of the cooking time reserve about 1 cup of pasta cooking water. We will need only 1/2 cup for this recipe but it's always good to have more on hand if you need to dilute the sauce.
Add the 1/2 cup of the water to the pan and whisk intensively to combine it with butter and olive oil. Set aside. Reserve the remaining pasta cooking water.
Add the cooked pasta to the pan and toss it with the sauce. Let stand for about a minute or two, letting it cool slightly before adding the cheese.
Add the cheese and stir very intensively with kitchen tongs or two forks until the cheese is melted, creamy, and creates a smooth silky sauce. You can put the pan on the burner while you do this and heat it over very low heat to help melt the cheese. If the cheese doesn't melt easily add some more reserved pasta cooking water. Heat the sauce gently over low heat until all the cheese is melted.
Taste the pasta and season with more pepper if necessary.