Cook the pasta according to the instructions on the package, drain and keep warm under cover.
Meanwhile blanch or steam the broccoli florets for about 5 minutes.
Chop the garlic and walnuts.
Heat the oil in a frying pan, then fry the garlic, walnuts and pumpkin seeds for 2-3 minutes, stirring constantly.
Roughly chop the broccoli florets, add to the frying pan together with 2-3 spoonfuls of the broccoli's cooking water. Toss well.
Take the pan off the heat. Add the grated lemon zest and juice, season with salt and pepper.
Mix the pasta with the broccoli & walnuts and, if necessary, add more cooking water to make it moist.
Serve with grated cheese if you like (such as Parmesan).