Heat the oil in a heavy-based frying pan over a medium-high heat. Add the garlic, courgettes and spring onions and cook, stirring, for 4–5 minutes until the courgettes are tender. Set aside.
Cook the pasta in a large saucepan of salted boiling water according to the packet instructions until al dente.
Meanwhile, crack the egg yolks into a bowl and season with salt and a generous grinding of pepper. Mix together with a fork.
Just before the pasta is ready, return the pan with the courgette mixture to the heat. Stir in the crème fraîche and bring to the boil.
Drain the pasta thoroughly, return it to the pan and immediately stir in the egg mixture, Parmesan and the creamy courgette mixture. Stir vigorously and serve immediately with a scattering of grated Parmesan.