Bring a large pot of well-salted water to a boil. Cook the spaghetti until al dente according to package instructions. Reserve 1 cup pasta water before draining.

In a bowl, whisk together the eggs, egg yolks, and grated pecorino until smooth. Set aside.

In a cold skillet, cook the pancetta over medium heat until the fat has rendered and the edges are crisp. Add the garlic cloves and cook for 1 minute, then remove and discard the garlic. Remove the skillet from heat.

Toss the hot drained pasta directly into the skillet with the rendered pork fat. Mix well to coat each strand.

Pour the egg and pecorino mixture over the pasta. Add about ¼ cup of the reserved hot pasta water.

Stir vigorously and continuously for 1–2 minutes until the sauce is glossy and creamy. Add more pasta water a splash at a time if the sauce tightens.

Crack fresh black pepper generously over the top and serve immediately.