Bring a large pot of water to a boil, season generously with sea salt, and cook the spaghetti until al dente.
In a small bowl, whisk together the whole egg, egg yolk, grated parmesan, and black pepper until well combined.
Heat a large skillet over medium heat and cook the pancetta until it is golden and the fat has rendered.
Add the diced chicken breast and minced garlic to the skillet, sautéing until the chicken is browned and fully cooked.
Reserve a small amount of the starchy pasta water, then drain the pasta and add it to the skillet, tossing to coat in the pancetta fat.
Turn off the heat and remove the pan from the burner to ensure the eggs create a sauce rather than scrambling.
Slowly pour in the egg mixture while tossing the pasta constantly, adding a splash of pasta water as needed to reach a silky consistency.
Season with the remaining sea salt and serve immediately while the sauce is warm and glossy.