Bring a large pot of water to a boil and season with sea salt, then cook the chickpea spaghetti until al dente.
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.
In a small bowl, whisk together the large egg, egg whites, grated Pecorino Romano, and black pepper until fully combined.
Reserve 0.25 cup of the starchy pasta water before draining the spaghetti.
Add the minced garlic to the skillet with the pancetta and cook for 30 seconds until fragrant.
Turn off the heat and add the hot pasta to the skillet, tossing well to coat the strands in the pancetta fat.
Slowly pour the egg and cheese mixture over the pasta while whisking or tossing constantly to create a creamy sauce without scrambling the eggs.
Add the reserved pasta water a tablespoon at a time if needed to reach a glossy consistency, then serve immediately.