Bring a large pot of salted water to a rolling boil. Add the spaghetti and cook according to package directions until al dente. Reserve about 1.5 cups of the starchy pasta water before draining.
While the pasta cooks, prepare the other components. In a large skillet over medium heat, cook the diced pancetta until crispy. Remove the pancetta with a slotted spoon and set aside on a paper towel-lined plate, leaving the rendered fat in the skillet. If you're using leaner bacon and there isn't much fat, add the olive oil.
Add the bite-sized chicken pieces to the skillet with the pancetta fat. Season lightly with salt and pepper. Cook, stirring occasionally, until the chicken is golden brown and cooked through, about 5-7 minutes. Add the minced garlic during the last minute of cooking until fragrant.
In a medium bowl, whisk together the whole eggs, egg yolks, Pecorino Romano cheese, Parmesan cheese, and the 1/2 teaspoon of black pepper until well combined and smooth. This is your creamy sauce base.
Once the pasta is drained, immediately add it to the skillet with the chicken and garlic. Toss to combine.
Remove the skillet from the heat. This is crucial to prevent the eggs from scrambling. Gradually pour the egg and cheese mixture over the hot pasta, tossing constantly with tongs. The residual heat from the pasta and skillet will cook the eggs and create a creamy sauce.
Slowly add the reserved pasta water, a few tablespoons at a time, while continuing to toss, until the sauce reaches your desired creamy consistency. It should coat the pasta beautifully without being too thin.
Stir in the crispy pancetta. Taste and adjust seasoning with salt and more black pepper if needed.
Serve immediately, garnished with extra grated cheese and fresh parsley, if desired.