Put a large pan of well-salted water onto the boil (it should taste pleasantly salty). Cut the florets off the broccoli and halve the larger ones – you can leave the small ones whole.
Peel and discard the tough skin from the broccoli stalk and then cut the remaining stalk into strips about 1cm thick. Cut the strips in half lengthways and widthways so you have roughly thumb-sized rectangles.
Once the water is boiling, tip in the broccoli florets and stalk pieces and let them cook for about 5 mins until quite tender – you should be able to skewer them on a fork easily.
Meanwhile, put a large frying pan with nice high sides over a low-medium heat and add the olive oil. Roughly chop the olives. Now you’ve got two choices: either slightly crush the garlic but leave it whole to be removed later (milder), or chop the garlic and add the whole lot (stronger). Either way, add the garlic to the oil along with the olives, chilli and anchovies, if using.
Let the garlic cook gently for a couple of minutes, but don't let it go brown. The anchovies will dissolve into the oil and by now your broccoli should be ready, so use a slotted spoon to scoop it out of the water and put it straight into the pan with the garlic, making sure you get a good splash of the water in there as well.
Add the pasta to the broccoli water and cook until al dente. Meanwhile, mash the broccoli with the back of a wooden spoon to create a creamy sauce with the oil and water. Squeeze in the lemon juice and then turn the heat off until the pasta is cooked.
Once dente, add the pasta to the pan with the plus a splash of pasta water. Mix well over a medium heat until the pasta is saucy and well coated. Taste and add more if needed.