Bring a large pot of water to a boil and season with the sea salt.
Cook the dry spaghetti until just al dente, reserving 0.25 cup of the starchy pasta water before draining.
While the pasta cooks, whisk together the whole eggs, egg whites, Pecorino Romano, and black pepper in a small bowl until smooth.
In a large skillet over medium heat, sauté the diced pancetta until crispy and the fat has rendered.
Add the minced garlic to the skillet and cook for 30 seconds until fragrant, then remove the skillet from the heat source.
Add the hot, drained pasta to the skillet with the pancetta, then slowly pour in the egg mixture while tossing constantly to create a creamy emulsion.
Gradually add the reserved pasta water one tablespoon at a time as needed to reach a glossy consistency, ensuring the heat from the pasta thickens the eggs without scrambling them.
Garnish with fresh parsley and serve immediately in a warm bowl.