advice on a yellow broom

With brooms, you just trim them after they've flowered. Don't cut into old wood, just this year's growth.

thanks, how will I know what is old growth or this years

Well, the flowers grew on it! It will be brighter green, but I wouldn't cut back that far unless the plant is too big.

Agree just trim after plant has flowered. Just one point Brooms have a life span of about 10 years then they won't flower again and need to be replaced.

Dead easy from cuttings and seed too.
As far as pruning is concerned, I cut ours back by about 2/3 after flowering. That is, every GREEN shoot is cut back to about 1/3 of its length. As long as you leave a short length of green stem then it will grow new shoots and flower again. If you do not prune then what you end up with is a tall bush with all the flowers at the top and an ugly naked base.