Bring a pot of salted water to a boil and cook the whole wheat spaghetti according to package directions until al dente.
While the pasta cooks, whisk together the large egg, egg whites, and grated parmesan in a small bowl until smooth.
In a large skillet over medium heat, sauté the diced pancetta until it becomes golden and crispy.
Add the minced garlic and shredded chicken to the skillet, stirring for 1 minute until the garlic is fragrant.
Reserve 0.25 cup of the pasta cooking water, then drain the pasta and add it directly to the skillet with the pancetta.
Remove the skillet from the heat immediately to prevent the eggs from scrambling.
Pour the egg mixture over the pasta, tossing quickly and continuously while adding splashes of the reserved pasta water to create a creamy, velvety sauce.
Season with cracked black pepper and sea salt before serving immediately.