Desserts are not really my forte but I'll have a go and say what I would do in the same situation. I hope you have some freezer space available.
Bramley apples are a very British thing, often called 'cooking apples'. (I've never seen Bramleys outside the UK.) A lot of chefs, myself included, aren't keen on Bramleys because of the texture. They turn to mush very quickly and easily. Thus we tend to use dessert apples for cooking in preference to Bramleys. Who wants to eat mushy baby food?
To prevent the brown colour you need acidulated water, which could be as simple as squeezing some lemon juice onto the fruit once it's peeled. I would then use the apples for any normal cooking purpose, eg apple sauce (to go with roast pork or pork chop, etc), apple crumble. Anything really where many Brits would reach for the Bramleys. Do take care, though, because they're much sweeter than Bramleys so don't add sugar unless you're absolutely sure the dish needs it.
Hope this helps.
