I interpreted banana cake kind of loosely to cover banana bread - it's a quickbread which is more like cake than, say, sandwich bread, so I figured that would count.

But my favorite use for ripe (i.e. brownish-yellow) bananas is to make 'ice cream' with them. Slice, freeze until solid, blitz with a spoonful of milk and a drop of vanilla extract until consistency is like soft-serve ice-cream. YUM!