Bring a large pot of water to a rolling boil and season generously with salt until it tastes like seawater.

Cook the spaghetti according to package directions until al dente; reserve 1 cup (240ml) of starchy pasta water before draining.

While the pasta cooks, whisk the eggs, egg yolk, and grated cheese in a medium bowl until a thick paste forms, then set aside.

In a large skillet over medium-high heat, add olive oil and sear the chicken pieces until golden brown and the internal temperature reaches 165°F (74°C). Remove chicken from the pan and set aside.

In the same skillet, add the diced pancetta and cook over medium heat until the fat renders and the meat becomes crispy.

Add minced garlic to the skillet with the pancetta and sauté for 30 seconds until fragrant but not browned.

Add the drained pasta and the cooked chicken back into the skillet with the pancetta, tossing to coat in the rendered fat.

Remove the skillet from the heat source entirely to prevent the eggs from scrambling upon contact.

Slowly pour the egg and cheese mixture over the pasta while tossing vigorously with tongs. Gradually add reserved pasta water, one tablespoon at a time, until the sauce emulsifies into a creamy, glossy coating.

Season with cracked black pepper and parsley, then serve immediately on warmed plates.