Banana and Demerara cake

Guests love to come back to a really warm chalet after a day on the slopes, but having the heating on high means that fruit in the fruit bowl ripens fast. Chalet hosts therefore keep bananas in the fridge, but if bananas get too cold they go black and nobody will want them. What to do with all the unwanted bananas? This recipe is very easy and will tolerate bananas from not so ripe to completely over-ripe.