3 Tablespoons . kosher salt, plus more
4 oz. pancetta (Italian bacon), or bacon
3/4 Cup Parmesan
4 large egg yolks
2 large eggs
Freshly ground black pepper
2 Tablespoons extra-virgin olive oil
1 lb. spaghetti, bucatini, or rigatoni
Heat 6 qt. water in a large pot over high. When water starts to steam, add 3 Tablespoons salt and cover pot with a lid (this will bring water to a boil faster).
While you are waiting on the water, do a little prep. Remove 4 oz. pancetta or bacon from packaging and cut into about 1x1/4" strips. Finely grate 3/4 Cup cheese and set aside 1/4 Cup of cheese for later.
Whisk 4 egg yolks and 2 whole eggs in a medium bowl until no streaks remain, then stir in remaining grated cheese, 1/2 Cup. Add several cranks of pepper and set aside.
Working next to pot, heat 2 Tablespoons oil in a large Dutch oven or other heavy pot over medium. Add the pancetta or bacon, and cook, stirring occasionally, until crisp around the edges, 7–10 minutes.
Remove pot from heat. Using a wooden spoon, fish out pancetta or bacon and transfer to a small bowl. Pour fat into a heatproof measuring cup, then add back about 3 Tbsp. to pot. Discard any remaining fat.
Cook 1 lb. pasta in boiling water, stirring occasionally, 2 minutes shy of package instructions. Just before pasta is finished, scoop out 1 3/4 cups pasta cooking liquid with same heatproof measuring cup.
Add 1 Cup reserved pasta cooking liquid to Dutch oven and bring to a boil over medium-high. Drain pasta in a colander, then transfer to Dutch oven.
Cook pasta, stirring constantly and vigorously, until al dente and water is reduced by about half, about 2 minutes. Remove pot from heat.
Whisk 1/4 Cup pasta cooking liquid into reserved egg mixture, then very slowly stream into Dutch oven, stirring constantly, until cheese is melted and egg is thickened to form a glossy sauce. Season with salt, if needed. Thin sauce with remaining 1/2 Cup pasta cooking liquid, adding a tablespoonful at a time, until it's the consistency of heavy cream (you most likely won’t use all of it).
Mix in the pancetta or bacon, and divide pasta among bowls. Top with pepper and reserved cheese.