Cut the guanciale into batons, about 0.5 cm (1/5 inch) thick.

In a large bowl, whisk the eggs and egg yolks until well combined. Stir in the finely shredded Parmigiano Reggiano and black pepper until smooth. Set aside.

Bring 4 liters (4 quarts) of water to a boil in a large pot. Add the salt and cook the spaghetti according to the package directions. Reserve 1 cup of pasta cooking water before draining.

Heat a non-stick skillet over medium-high heat. Add the guanciale and cook for 4-5 minutes until golden and crispy. If using garlic, add it during the last minute of cooking for a subtle aroma.

Add the drained spaghetti directly into the skillet with the guanciale. Toss to coat the pasta in the flavorful fat.

Transfer the pasta and any residual fat into the bowl with the egg mixture. Add 1/2 cup of reserved pasta cooking water and stir vigorously with a wooden spoon for about 1 minute. Watch as the sauce transforms into a creamy texture that clings to the pasta strands.

Divide the pasta into warm bowls. Garnish with extra Parmigiano Reggiano, a sprinkle of black pepper, and chopped parsley for a fresh pop of flavor. Serve immediately and enjoy!