Bring a large pot of water to a boil, add the sea salt, and cook the whole wheat spaghetti until just al dente.
While the pasta cooks, place the diced pancetta in a cold skillet and set the heat to medium, cooking until the fat renders and the meat becomes golden and crispy.
In a separate mixing bowl, whisk together the whole egg, egg whites, finely grated Pecorino Romano cheese, and freshly cracked black pepper until smooth.
Before draining the pasta, reserve approximately half a cup of the starchy pasta water.
Drain the noodles and immediately add them to the skillet with the pancetta, tossing them in the rendered fat over low heat.
Remove the skillet from the heat entirely and slowly pour the egg and cheese mixture over the pasta.
Toss the pasta vigorously and constantly; the residual heat will cook the eggs into a creamy sauce without scrambling them.
Add a small amount of the reserved pasta water as needed to reach a silky, glossy consistency.
Garnish with chopped fresh parsley and serve immediately while hot.