Bring a large pot of salted water to a boil and cook the chickpea spaghetti according to package directions until 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 pancetta is golden and crispy.
Add the smashed garlic clove to the skillet with the pancetta for the last 2 minutes of browning to infuse the oil, then remove and discard the garlic.
In a small bowl, whisk together the whole egg, egg whites, and finely grated Pecorino Romano cheese until well combined.
Before draining the pasta, reserve 0.25 cup of the starchy pasta water.
Drain the pasta and immediately add it to the skillet with the pancetta, tossing to coat in the rendered fat while the heat is off.
Slowly whisk the reserved hot pasta water into the egg mixture to temper the eggs, preventing them from scrambling.
Pour the tempered egg mixture over the pasta, tossing constantly for 1-2 minutes until the sauce thickens into a creamy glaze from the residual heat.
Finish with a generous amount of freshly cracked black pepper and serve immediately.