Fill a large pot with water and bring it to a boil. Add the salt to the boiling water.
Cook the spaghetti according to package instructions until al dente. Reserve 1 cup of pasta cooking water before draining, then set the pasta aside.
Dice the pancetta into 1/4-inch pieces.
Heat a large skillet over medium heat. Add the diced pancetta and cook, stirring occasionally, until it becomes crispy.
Transfer the cooked pancetta to a paper towel-lined plate using a slotted spoon. Leave the rendered fat in the skillet.
In a medium bowl, separate the egg yolks from the whites. Save the whites for another use or discard them.
Whisk the egg yolks with most of the grated Parmigiano Reggiano. Reserve some of the cheese for garnish.
Add freshly cracked black pepper to the egg and cheese mixture and continue whisking until smooth.
Add the hot, drained spaghetti to the skillet with the pancetta fat. Toss the pasta over low heat until evenly coated.
Remove the skillet from the heat. Quickly pour the egg yolk and cheese mixture over the pasta.
Toss the pasta constantly to combine the ingredients and form a creamy sauce.
If the sauce is too thick, gradually add the reserved pasta water, a little at a time, until it reaches your desired consistency.
Add the crispy pancetta back to the skillet. Toss everything together to mix well.
Serve immediately, dividing the pasta into portions. Garnish with the reserved Parmigiano Reggiano and additional black pepper, if desired.