Photo: Tara Fisher
Heat the olive oil in a frying pan over a low heat and gently soften the garlic for a couple of minutes. Set aside.
Whisk together the 4 egg yolks, 1 whole remaining egg and two-thirds of the grated cheese in a small bowl. Add the garlic and season with lots of black pepper.
Cook the pasta according to the instructions on the packet. Add the asparagus for the last 3-4 minutes. Drain, saving half a mugful of the cooking water. Return the pasta and asparagus to the pan and add the egg and cheese mixture, stirring constantly. Add enough of the reserved cooking water to create a creamy sauce that coats the pasta. Stir in the basil, then scatter over the pine nuts and serve with the remaining cheese.