Melt the butter in a medium non stick saucepan then add the grated onion and as good pinch of salt. Cook over a gentle heat, stirring often, for about 5 minutes until the onions have softened but not browned.
Sprinkle the flour over the top and stir for a minute or two until it starts to turn a pale gold. Now gradually beat in the cider until the sauce is smooth. When all the cider has been added bring to a boil then reduce the heat a little and simmer for another 5 minutes, stirring occasionally to stop it sticking.
Beat in the mustard then stir in the cheese until everything is thoroughly melted. Remove from the heat then carefully taste ( its hot…) and season. If you like you can leave it to cool at this stage then keep it in the fridge for a couple of days until you need it.
When you are ready to eat spoon half the mixture thickly over your pieces of toast and cover with a layer of overlapping apple slices. Spread the rest of the rarebit mixture over the top and grill for 1-2 minutes, or until the top is bubbling and speckled with brown.