Heat 6 qt. water in a large pot over high heat. When water starts to steam, add 3 Tbsp. Diamond Crystal or 1 Tbsp. plus 2¼ tsp. Morton kosher salt and cover pot with a lid.

Slice 4 oz. guanciale, pancetta, or bacon into about 1x¼" strips. Finely grate 2 oz. Parmesan or Pecorino Romano and set aside a quarter of the cheese for later.

Whisk 2 large eggs plus 3 large egg yolks in a medium bowl until no streaks remain, then stir in bulk of the grated cheese. Add several cranks of freshly ground black pepper and set aside.

Heat 2 Tbsp. extra-virgin olive oil in a large Dutch oven or other heavy pot over medium. Add sliced guanciale, pancetta, or bacon and cook, stirring occasionally, until crisp around the edges, 7–10 minutes.

Remove pot from heat. Using a wooden spoon, scoop out pork and transfer to a small bowl. Pour fat into a heatproof measuring cup, then add 3 Tbsp. of rendered fat back to pot.

Cook 12 oz. spaghetti in salted boiling water, stirring occasionally, 2 minutes shy of package instructions. Just before pasta is finished, scoop out 1¾ cups pasta cooking liquid.

Add 1 cup reserved pasta cooking liquid to Dutch oven and bring to a boil over medium-high. Drain spaghetti 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 ¼ cup reserved pasta water into 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 kosher salt, if needed. Thin sauce with remaining ½ cup pasta cooking liquid, adding a tablespoonful at a time, until it's the consistency of heavy cream.

Mix in pork and divide pasta among bowls. Top with pepper and reserved cheese.