Bring a large pot of salted water to a boil. Add the spaghetti and cook until almost al dente (about 2 minutes less than package instructions).
While the pasta is cooking, mix the egg, egg yolks, cheese, salt and pepper in a medium bowl. Reserve.
Heat the oil in a large skillet, over medium-high heat. Add the diced pancetta and cook until crispy and golden brown, about 5 minutes. Remove the pan from heat and reserve the pancetta with about 3 tablespoons of the rendered fat.
When the pasta is done, drain it in a colander set over a large mixing bowl, letting the hot pasta water heat the bowl. Reserve 1 cup of the starchy water.
Discard the water and use that bowl to toss the pasta with the pancetta, reserved fat, egg mixture and 1/2 cup pasta water. Work quickly, tossing vigorously and adding more pasta water if necessary, until the sauce is silky and the cheese has melted completely. You can add more salt and pepper if needed.
Garnish with chopped parsley and serve with extra Parmigiano Reggiano at the table.