Bring a large pan of salted water to the boil, add the broccoli and cook for 2-3 mins until just tender. Use a slotted spoon to remove, then set aside. Bring the water back to the boil, add the pasta and cook following pack instructions.
Heat the olive oil in a frying pan, add the courgettes and cook over a high heat for 3-4 mins until starting to turn golden, tip in the broccoli and continue to cook for 1 min until warmed through.
Drain the pasta, reserving about 2 tbsp of the cooking water, then add pasta and cooking water to the pan with the vegetables and the gremolata. Mix well and serve.