Most people once the broccoli flowers cut that off, and then cut out the plant. I for one was one was one of them. Recently I have left them grow and once all the little flowers come up from the branches, then I would dig out the whole plant. This year I have left them in and at least once per week I can go out and get 2 handfuls of bits- or broccolini if you like. I will leave them and see what happens. I would say for certain that if you leave it and continually harvest them you will get 3 times the amount than if you only harvesting once.
Its nice to have wood at the back door, I have found another use- apart from heating the house, heating the hot water, drying the clothes and cooking my food- the lounge is warm enough to “Brew beer” BOOM!!!!!! The wood is from a couple of farmers properties that I am related to, they dont want the wood lying around and its already dead. Sustainable- well sort of!