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Heat a large skillet over medium-low heat. Add the diced pancetta—no oil needed—and cook, stirring occasionally, until golden brown and crispy, about 5 minutes. Transfer the pancetta to a paper-towel–lined plate, leaving the rendered fat in the skillet.
In a large mixing bowl, whisk together the egg yolks and the whole egg. Add the grated Pecorino Romano and a generous grind of fresh black pepper, whisking until smooth and creamy.
Bring a large pot of water to a boil. Season generously with coarse salt. Add the spaghetti and cook until al dente, according to the package instructions.
Before draining, reserve about 2/3 cup of the pasta cooking water. Drain the spaghetti, then immediately add it to the skillet with the pancetta fat, tossing to coat evenly.
Remove the skillet from the heat. Quickly pour in the egg-and-cheese mixture and a splash of the reserved pasta water. Stir or toss vigorously until the sauce becomes smooth and silky, adding more reserved water as needed to reach your desired consistency. Then fold the crispy pancetta back in.
Divide the pasta among plates and serve immediately with extra grated Pecorino Romano and an additional grind of black pepper on top.