This is such a delicious and comforting dish when executed well, but can be very tricky to do right.
The basic building blocks will be eggs, egg yolks, cheese, black pepper, and cured pork fat.
The tricky part comes from getting the eggs to coat the pasta without turning into scrambled eggs - and for that, we turn to tempering.
Basically, how to cook eggs without curdling them. In this case, we are looking for a thick, unctuous sauce to coat every bit of the pasta we choose.
Tempering involves gentle, indirect heat and lots of movement.
In this case, the eggs, cheese, and pepper are combined in a large bowl and placed over the pasta water pot as we turn it on. But, what I learned, is that the bowl can neither touch the water or the pot, and the water cannot be boiling. Any of these three rules violated, and you are on your way to scrambled eggs.
Take a large piece of foil, and crumple it into a ring around the lip of your pot. Place the bowl (metal is probably best) on the foil, bring the water to a bare simmer, and ensure its not touching the bowl.
Now you can whisk constantly. The mixture should deepen in color, and thicken. It's done when it is as thick as you want it. Keep in mind that it doesn't need to be a sludge. When you combine it with the pasta, fat, and starchy pasta water, it will thicken more and emulsify. Mine came to the consistency of thin pancake batter - but not quite as thin as crêpe batter.
This is a technique driven dish, and only has a few ingredients, so they need to be the best quality you can find.
Eggs, and specifically egg yolks, do the heavy lifting in this sauce to create an emulsified, unctuous, sauce. They, along with the cheese and guanciale, bring umami to the table. So select nice eggs with nice, deeply colored egg yolks.
Good Parmigiano-Reggiano is crucial to making this sauce. Salty, savory, sharp cheese that adds dimension to the dish. For even more dimension, and some slightly funkier and grassier notes, replace 1/3 of the cheese with Pecorino Romano. And of course extra for the top.
Black pepper should always be freshly ground. Use your discretion as to the grind size and amount, but you want to know it's there. The pepper helps cut through all the fat in this dish - which is pretty much everything else - so it needs to be a heavy amount. Always keep a good supply of high quality black peppercorns. I really like these Tellicherry variety.
Guanciale is cured pork jowl. Its mostly fat with a stripe of muscle in the center, and is flavored lightly with warm spices in the curing mixture. This needs to be cut into large pieces and slowly rendered in a pan with olive oil. Your goal is to extract the fat from the lardons and then let them crisp. The crispy, salty crunch of these in the dish are a nice balance to the pasta.
Starchy pasta water is the catalyst to help everything emulsify. The water in the egg whites and the pasta will not want to mix with the fats of the yolks, olive oil, cheese, and pork fat. But the starches in the water help bring everyone together into a glossy, smooth, thick glaze.
Pasta is not worth the calories if it isn't high quality. If using extruded, buy the type made with bronze dies so that its still rough looking. We need that rough exteriour to release extra starch. Normally I would not recommend fresh for this, but do what you want! Find a unique shape and use that.