I used to wait until the stalks lost all their leaves - cut them of (or snap them at the base), uproot and dry off for a while, then put them in paper bags or newspaper and put in a cool place until late Spring. You have to search for weevils as I did this for a few years and the corms got enormous but went rotten when I discovered the blighters inside them.

I'v always been confused with begonias are ALL the large ones corms?

I think so. The others are bedding begonias which don't have a corm and can't be overwintered.