Bring a large pot of water to a boil and season with the sea salt.
Cook the whole wheat spaghetti according to package directions until it reaches an al dente texture.
While the pasta cooks, place the diced pancetta in a large skillet over medium heat and sauté until the fat renders and the meat is crispy.
Add the smashed garlic clove to the skillet with the pancetta for the final 2 minutes of browning to infuse the oil, then discard the garlic.
In a medium mixing bowl, whisk together the whole eggs, egg whites, grated Pecorino Romano, grated Parmesan, and black pepper until well combined.
Reserve approximately 0.25 cup of the starchy pasta cooking water before draining the spaghetti.
Immediately add the hot, drained pasta to the skillet with the pancetta and toss to coat in the rendered fat.
Remove the skillet from the heat source entirely to prevent the eggs from scrambling.
Pour the egg and cheese mixture over the pasta, tossing rapidly with tongs while adding the reserved pasta water one tablespoon at a time until a smooth, glossy sauce forms.