Bring a large pot of water to a boil and season with sea salt.
Cook the chickpea spaghetti according to package directions until al dente.
While pasta cooks, whisk the whole eggs, egg whites, grated Parmesan, and Pecorino Romano in a small bowl until smooth.
In a large skillet over medium heat, sauté the diced pancetta until the fat has rendered and the meat is golden and crispy.
Reserve 0.25 cup of the hot pasta water, then drain the spaghetti.
Add the pasta to the skillet with the pancetta and toss to coat in the rendered fat, then remove from heat.
Slowly whisk 2 tablespoons of the hot pasta water into the egg mixture to temper it, preventing the eggs from scrambling.
Pour the egg mixture over the pasta, tossing constantly with tongs until a creamy, glossy sauce forms.
Season with freshly cracked black pepper and serve immediately.