Bring a large pot of water to a boil, season with sea salt, and cook the chickpea spaghetti according to package instructions until al dente.
While the pasta cooks, dice the pancetta and place it in a large skillet over medium heat, sautéing until it becomes golden and crispy.
In a medium bowl, whisk together the whole eggs, egg whites, grated Pecorino Romano, and Parmesan cheese until the mixture is smooth and well combined.
Add the minced garlic to the skillet with the pancetta and cook for 30 seconds until fragrant, then immediately remove the skillet from the heat.
Reserve 0.25 cup of the starchy pasta water, then drain the spaghetti and add it directly to the skillet with the pancetta and garlic.
Working quickly, pour the egg and cheese mixture over the pasta while tossing constantly with tongs; the residual heat will cook the eggs into a creamy sauce without curdling them.
Slowly add the reserved pasta water one tablespoon at a time until the sauce reaches a glossy consistency, then finish with a generous amount of freshly cracked black pepper.