Preheat oven to 375° F. Grease 15 x 10-inch jelly-roll pan. Line the pan with parchment paper.
With an electric mixer, beat eggs and sugar in a mixing bowl until thick and smooth, about 3 minutes.
Add the vanilla and banana. Mix together until incorporated.
Mix together the flour, salt, baking soda, and baking powder. Slowly add it to the egg mixture. Do not over-mix.
Spread evenly into the prepared pan.
Bake for 13 to 15 minutes (more or less depending on the size of the pan,) or until the top of the cake springs back when touched.
While the cake is baking, sprinkle the confectionery sugar over the towel.
Immediately after removing the cake from the oven turn the cake out onto the towel carefully.
Roll up the cake from the short side into a roll.
Let the cake cool in the towel.