Set out the sauce ingredients before the hob goes on. A cheese sauce asks for attention once the butter melts, and trying to measure flour or grate cheese mid-sauce is the quickest way to make everyone feel rushed. Let the child do those jobs first, then put the milk in a small jug that is easy to control.
Cut the broccoli into genuinely small florets. Children often break off impressive tree-sized pieces, but smaller pieces cook at the same pace and distribute through the pasta instead of taking over the bowl. Peel and slice the tender stalk too if your child is happy with the extra cutting job.
Treat draining as a named adult job before cooking begins. Pasta water is heavy and steamy, and broccoli water can splash just as easily. The child can place the colander in the sink and stand back, then take ownership again when the safe, drained ingredients are ready.
For a smooth sauce, stir the flour into melted butter until no dry flour remains, then add only a small splash of milk. Whisk that smooth before the next splash. The sauce may look oddly thick at first; reassure the child that each addition loosens it, and keep scraping around the edge of the pan.
Look for a sauce that coats the back of a spoon rather than relying only on a timer. If it is too thick, whisk in a splash of milk or reserved pasta water. If it is thin, keep it over gentle heat and stir for another minute. Add the cheese off the heat so it melts without the sauce becoming greasy.
Hand the ending back to the child. Tip the drained pasta and broccoli into the sauce, or pour the sauce over them in a larger bowl, then let the child fold everything together slowly. A short cooling pause protects mouths and gives the sauce time to cling to the pasta.