Bring a large pot of filtered water to a rolling boil and season generously with the sea salt to enhance the pasta's flavor.
Add the chickpea pasta and cook according to the package instructions until al dente, ensuring you reserve 0.5 cup of the starchy pasta water before draining.
While the pasta is boiling, place the diced pancetta in a cold, large skillet and set the heat to medium to slowly render the fat until the bits are golden and crispy.
Stir the minced garlic into the skillet with the pancetta and sauté for just 30 seconds until fragrant, then immediately remove the pan from the heat source.
In a medium glass bowl, whisk together the whole egg, egg yolk, egg whites, grated Pecorino Romano, and black pepper until the mixture is uniform and creamy.
Gradually whisk 2 tablespoons of the hot reserved pasta water into the egg mixture to temper it, which ensures a smooth sauce rather than scrambled eggs.
Add the drained pasta directly into the skillet with the pancetta and garlic, tossing well to coat the noodles in the rendered fat.
Pour the tempered egg and cheese mixture over the pasta and toss vigorously off the heat, adding small splashes of the remaining pasta water until a glossy, silk-like sauce forms.