Preheat oven ro 375 degrees.
In a large bowl, mix mashed bananas, eggs, melted butter, sugar and vanilla essence, to form a smooth batter.
Mix in flour and baking powder well, and pour the batter into a greased baking tin - either an 8-inch round pan or an 8-inch square pan.
Bake for 20-25 minutes till the cake a cooked through. You can poke a toothpick into the center of the cake, and if it comes out clean, that means it's cooked through.