Bring a large pot of water to a boil and add the sea salt.
Cook the spaghetti according to package directions until al dente.
While the pasta cooks, whisk the whole egg, egg whites, grated Pecorino Romano, and black pepper in a small bowl until well combined.
In a large skillet over medium heat, sauté the diced pancetta until the fat renders and it becomes crispy.
Add the smashed garlic clove to the skillet with the pancetta for the last 2 minutes to infuse the oil, then remove and discard the garlic.
Reserve 0.25 cup of the starchy pasta water, then drain the spaghetti.
Turn off the heat under the skillet and add the hot pasta directly to the pancetta, tossing to coat in the rendered fat.
Slowly pour the egg and cheese mixture over the pasta while whisking or tossing constantly to create a creamy sauce without scrambling the eggs.
Add the reserved pasta water a tablespoon at a time if needed to reach a glossy, velvety consistency.
Garnish with fresh parsley and serve immediately.