Cook the pancetta in a large nonstick skillet over medium heat until crisp and the fat has rendered, 5 to 7 minutes. Remove the pancetta to a paper-towel-lined plate and set aside. Add the onions to the pan with the drippings and cook until translucent, 3 to 5 minutes. Season with salt and pepper, and then reduce the heat to keep warm.
Separate the eggs and place the yolks in a large bowl (reserve the whites to use in another recipe). Whisk together the egg yolks and half the Parmigiano-Reggiano and season with salt and pepper. Add the egg mixture to a large stainless bowl with the onions and mix well.
Cook the pasta in salted, boiling water until al dente (according to pasta directions). When the pasta is just about finished, strain the pasta and transfer directly from the pot of water to the mixing bowl with the onions. Using tongs, mix well so the egg mixture coats the pasta evenly and cooks from the residual heat. Add about 3/4 cup of pasta water to fortify the sauce. Fold in the remaining Parmigiano-Reggiano, crisped pancetta (reserve a little for garnish) and season with salt and pepper.
Serve immediately, garnished with the reserved pancetta and parsley.