Beat butter, sugar and vanilla essence till the mixture is light and fluffy.
Add the mashed bananas to the above mixture
Add all purpose flour, baking powder and baking soda in a bowl and whisk it well.
Fold in the flour into the butter-sugar mixture little by little.
Once its well mixed, transfer it to 8 inch baking tray and bake it for 20-25 mins or till it is done. Alternately you can cover it with aluminium foil and steam it in the cooker for about or till it is done.
If you like it rich, you can frost the with cream cheese or chocolate ganache or any other frosting of your choice.
Recipe by Spice Counter at http://spicecounter.com/bakes/eggless-banana-cake/