Fill a large pan with salted water and bring to a boil.
While waiting for it to reach a rolling boil, break the broccoli into bite sized florets and slice the stalks into small chunky pieces.
Add the pasta to the boiling water and cook for 5 minutes then add the broccoli pieces and stalks. If using frozen broccoli let the pasta cook for 7 minutes before adding it. Don't stir it. We want to keep the broccoli on the top. Cook until the pasta is tender (another 3 to 5 minutes depending on the variety).
While waiting add the rest of the ingredients to a blender.
Once the pasta is pretty much ready, scoop out about 2 cups or mug fulls of broccoli pieces using a slotted spoon. Don’t worry if you get a bit of water with them. Add them to the blender with the other ingredients and blend until smooth. You will end up with a thick, green, creamy sauce.
Scoop out a mug full of the pasta water and reserve, then drain the pasta and remaining broccoli before returning to the pan.
Spoon the sauce from the blender into the pasta and broccoli, along with about half a cup (120ml) of the reserved pasta water. Toss vigorously adding more pasta water as needed to thin.
Taste to check seasoning, adjust as necessary, then serve immediately.