Florets only, no stalk
What to keep and what to throw away when a brassica is allowed at all, and why the two parts of the same vegetable behave so differently.
A cauliflower is two different vegetables joined together. The floret is a dense head of undeveloped flowers with fine, short fibres that soften readily. The stalk and the thick core beneath it are structural, built from long tough strands designed to hold the whole head upright, and no amount of cooking turns them into anything a cautious gut should be asked to manage. Florets only, no stalk, is the instruction, and it is a real one rather than a refinement.
This is also the clearest example in the book of hospitals disagreeing. Some allow well-cooked florets and some leave brassicas out entirely. See brassicas before you cook either.
How to do it
Cut the head into quarters through the core, then cut the core away and put it in the compost along with the thick stems and the outer leaves. What you want is the button of curd at the top of each branch, with no more than a centimetre of stem attached. Break rather than slice where you can, because a break follows the natural join.
Cut the florets to an even size, no bigger than a walnut, then boil or steam them until soft rather than until tender.
The cue
A knife should slide into the thickest floret and meet nothing. If it stops, they need longer. A floret cooked properly for this diet is past the point most cooks would call ready, and it will break under a fork rather than holding together.
Common mistakes
Keeping the stalk because it seems wasteful. Undercooking, out of a reasonable dislike of soggy cauliflower, which is the wrong instinct in this one context. Roasting instead of boiling, which firms the outside. And forgetting the other half of the question, which is wind rather than fibre. Brassicas are gas-forming for many people, so if you have a stoma, try them on a day when that would not be a problem.