Add the olive oil to a large skillet and heat over medium-high heat. Once hot, cook the guanciale until browned and crisp. Add the garlic and saute with the guanciale for a few minutes. Remove the guanciale, garlic and rendered fat from the skillet and set aside for later use.
Bring a large pot of salted water to a boil. Cook the pasta until al dente, about 1 minute less than indicated on the package. With a ladle, scoop some of the hot water from the boiling pasta, and set aside in a small bowl. Drain the pasta in a colander and place it into a large serving bowl.
In a different bowl, beat the egg yolks, whole egg, Parmesan, pecorino and some freshly ground black pepper. Whisk in the cooled guanciale with all of the fatty delicious oil. While the pasta is still warm, quickly add the sauce to the pasta and toss very well, then add a couple of very small scoops of the reserved pasta water to help create the carbonara sauce and its unique creaminess.
Garnish the carbonara with some grated Parmesan and a drizzle of extra-virgin olive oil, and serve.