To make the caramel: Melt the butter in a saucepan. Add half a cup of brown sugar. Stir till it bubbles and well blended. Pour into the bottom of a round cake tin. Slice bananas lengthwise and place over the caramel mixture.
Cream butter and sugar and vanilla; add beaten eggs gradually; stir in sifted flour alternately with the milk. Spread over the bananas. Bake in a moderate oven (180 degrees) up to 45 minutes. Maybe less. Test with a straw. Turn onto a serving dish. Serve with cream or custard.