Cook the pasta in plenty of salted water following the instructions on the packet.
Boil the broccoli for 3 to 4 minutes. Put the cooked broccoli, basil, walnuts, garlic, lemon juice, Parmesan and olive oil into a blender jug, add a pinch of salt and blend to make a fairly thick pesto sauce.
When the pesto is ready, start adding the walnut drink bit by bit, stirring all the while, until you’ve thinned the creamy sauce down enough to give you the desired texture.
Pour the pesto over the strained pasta and serve with a little grated Parmesan cheese sprinkled over the top.