Bring a large pot of water to a boil, add a pinch of sea salt, and cook the chickpea spaghetti until just al dente.
While the pasta cooks, place the diced pancetta in a cold skillet and turn the heat to medium, rendering the fat until the meat is crispy and golden.
Add the minced garlic to the skillet with the pancetta for the last 60 seconds of cooking, then turn the heat to the lowest setting.
In a small mixing bowl, whisk together the whole egg, egg whites, and finely grated Pecorino Romano until a smooth, thick paste forms.
Reserve 0.25 cup of the starchy pasta cooking water before draining the spaghetti.
Add the drained pasta directly to the skillet with the pancetta and toss to coat in the rendered fat.
Remove the skillet from the heat entirely to ensure the eggs do not scramble; pour in the egg mixture and half of the reserved pasta water.
Toss the pasta vigorously and continuously, adding more pasta water if needed, until the sauce emulsifies into a creamy, glossy coating.
Garnish with freshly cracked black pepper and chopped parsley before serving immediately.