Bring a large pot of water to a boil, season with a pinch of sea salt, and cook the chickpea spaghetti according to package directions until al dente.
While the pasta cooks, whisk together the whole egg, liquid egg whites, and grated Pecorino Romano cheese in a small bowl until the mixture is uniform and smooth.
Place a large skillet over medium heat and add the diced pancetta, sautéing for 5 to 6 minutes until the fat has rendered and the meat is golden and crispy.
Add the minced garlic clove to the skillet with the pancetta and cook for just 60 seconds until fragrant, being careful not to burn it.
Reserve exactly 0.25 cup of the starchy pasta cooking water, then drain the remaining liquid from the spaghetti.
Turn off the heat entirely under the skillet to prevent the eggs from scrambling upon contact.
Add the hot, drained pasta directly into the skillet with the pancetta and garlic, tossing well to coat the strands in the rendered fat.
Slowly pour the egg and cheese mixture over the pasta while tossing vigorously with tongs, allowing the residual heat to cook the eggs into a creamy, glossy sauce.
Thin the sauce with the reserved pasta water one tablespoon at a time until your desired consistency is reached.
Season with freshly cracked black pepper and the remaining sea salt, then garnish with chopped fresh parsley before serving immediately.