You can avoid cooling the pan in
stage 7 by filtering the noisette butter immediately into another (cold) container.
You can also use slightly salted butter, but do be aware that the cooking to noisette stage will concentrate the initial saltiness.
You will have noticed how hot the butter gets towards the end of cooking — a bit like making
caramel — so I advise you not to make it when there are young children in the kitchen.