Remove the pistachios from their shells and chop them roughly. Wash and drain the sugar snap peas. Clean, wash and drain the broccoli and cut the broccoli florets from the stalk. Wash lemon hot, grate dry, grate peel thinly, halve lemon and squeeze juice.
Prepare the pasta in boiling salted water according to the instructions on the packet. Cook about half the broccoli in boiling salted water for about 5 minutes. Remove, rinse cold and puree finely with a hand blender.
Mix with pesto, lemon juice and zest. Season to taste with salt and pepper.
Cook the remaining broccoli in boiling salted water for about 5 minutes until al dente. After approx. 3 minutes add sugar snap peas, finish cooking and pour into a sieve. Drain the pasta in a sieve and put it back into the pot immediately.
Stir in the pesto. Fold in vegetables. Arrange pasta on plates and sprinkle with pistachios.