First make the gremolata. Mix all the ingredients together in a bowl.
Heat the oil in a nonstick frying pan over a high heat, add the courgettes and cook, stirring frequently, for 10 minutes, or until browned. Add the spring onions and cook, stirring, for 1–2 minutes.
Meanwhile, cook the pasta in a large saucepan of boiling water according to the packet instructions until al dente.
Drain the pasta thoroughly and tip into a serving bowl. Add the courgette mixture and the gremolata and toss well. Serve immediately with a scattering of Parmesan shavings.