Bring a large pot of salted water to a boil and cook the chickpea spaghetti until al dente.
While the pasta cooks, add the diced pancetta to a cold skillet and cook over medium heat until golden and crispy.
Add the minced garlic to the skillet and sauté for 30 seconds until fragrant, then remove the pan from the heat.
In a medium bowl, whisk together the whole eggs, egg whites, Pecorino Romano, and black pepper until combined.
Reserve 0.5 cup of the starchy pasta water before draining the spaghetti.
Transfer the hot pasta to the skillet with the pancetta, tossing to coat the noodles in the rendered fat.
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 vigorously and adding more pasta water as needed until a velvety, glossy sauce forms.