Begin by heating the water in a large pot over medium-high heat. Once it starts to simmer, add the coarse salt. When the water reaches a steady, rolling boil, add the pasta and stir briefly to prevent sticking.
In the meantime, take the guanciale, remove the rind and the peppered outer layer, and cut it into strips.
Let the guanciale sizzle in a non-stick pan over medium heat, without adding any oil. Allow it to cook until the fat has melted. At this point, pour the rendered fat into a bowl and return the guanciale to the heat to make it crispy. Then turn off the heat, drain the guanciale, and pat it dry on paper towels.
Grind the black peppercorns using a mortar and pestle until you achieve a medium grind; if you don’t have one, any other suitable tool will do. Toast the freshly ground pepper in a preheated dry pan over medium heat for a couple of minutes, until it releases a fragrant aroma.
Meanwhile, whisk the egg yolks together with the grated pecorino (reserving two tablespoons for later) and the toasted black pepper, leaving about a teaspoon aside for garnish. Mix well using a whisk.
Add one tablespoon of pasta cooking water and all of the reserved guanciale fat to the egg and cheese mixture to make it creamy and smooth.
Set aside a glass of pasta cooking water. Cook the pasta according to the time indicated on the package, but drain it about one minute earlier to keep it al dente. The best way to check is to taste it: it should be tender but still firm to the bite.
Transfer the pasta into a cold pan or bowl — you can use the one where you cooked the guanciale, but make sure it’s completely cooled down; otherwise, the heat will cause the egg to curdle. Add the egg yolk and pecorino cream along with a ladle of pasta water. Stir thoroughly to combine everything.
If the pasta seems too dry, add a bit more pasta water, aiming for a creamy consistency without it becoming too loose.
When the carbonara is nice and creamy, stir in the crispy guanciale (saving a few pieces for garnish) and plate. Finish with a sprinkle of pecorino and a dusting of black pepper.