Bring a pot of water to a boil and add the sea salt.
Cook the spaghetti according to package directions until al dente.
While pasta cooks, whisk the whole egg, egg whites, and grated Parmesan in a small bowl until smooth.
In a large skillet over medium heat, sauté the diced pancetta until the fat renders and it becomes crispy.
Add the minced garlic to the skillet with the pancetta and cook for 30 seconds until fragrant.
Reserve 0.25 cup of the pasta cooking water, then drain the spaghetti.
Turn off the skillet heat and add the hot pasta, tossing to coat in the rendered fat.
Quickly pour the egg and cheese mixture over the pasta while stirring constantly to create a velvety sauce without scrambling the eggs.
Add a splash of the reserved pasta water if needed to reach a silky consistency and season with fresh black pepper.