While the spaghetti are boiling in salted water (2 tsp (10 g) salt for every 4 1/5 cups (1 L) water), braise the bacon in olive oil.
Beat the egg yolks with black pepper and powdered parmesan. Remove the excess fat released by the bacon in the pan with a paper towel. Remove the pan from the heat. Add the al dente spaghetti to the pan. The pan needs to be on very low heat - you can even put it on top of the pot in which you boiled the spaghetti.
Add the yolks and stir. This is how you get the creamy consistency of Carbonara pasta and not by adding cream. There is no cream whatsoever in the original recipe.
Be careful with the temperature of the pan while adding the spaghetti and yolks. As I mentioned, the temperature needs to be low in order to obtain the cream and not scrambled eggs. The yolks themselves will cook adequately from the heat of the spaghetti around them.
Stir and distribute into pasta plates. Sprinkle with parmesan or pecorino cheese, as preferred. Add black pepper as well.
Notes: Another important factor for a good Carbonara, perhaps the most crucial, is the bacon or sausage that you use. In Italy, they make this pasta with Guanciale - a preserved sausage from the lower part of the jowls or face of the pig or with Pancetta bacon - which comes from parts of the pork breast. Look for these 2 products, learn more about their properties and how they look like.
If you can't find them, use a bacon that comes as close to them as possible. But do not use low quality bacon that comes in vacuum sealed packets under any circumstances.