Preheat the oven to 375°F.
Line a 15x10x1 jelly roll pan with parchment paper and spray with nonstick spray. Set it aside.
In a medium-sized mixing bowl whisk together the flour, baking soda, salt, and baking powder. Set it aside.
Using either a stand mixer or a medium-sized mixing bowl and a handheld mixer on high speed, beat the eggs, granulated sugar, and vanilla for 4 to 5 minutes until a frothy pale yellow.
Add in the mashed bananas and continue to mix on medium until well incorporated.
Fold in the flour mixture.
Using either a silicone spatula or an offset spatula to spread the cake batter evenly in the jelly roll pan.
Bake for 12 to 13 minutes.
Remove the cake from the oven. Run the tip of a sharp knife around the edges of the pan that were not covered by the parchment paper.
Heavily dust the tea towel with powdered sugar.
Immediately place the dusted tea towel powdered side down on top of the cake.
Lay the cutting board on top of the dusted tea towel. The cake pan will be hot, you will need to be careful to protect your hands. Quickly flip the cake pan over so that the cake is now on top of the dusted tea towel.
Carefully and slowly peel the parchment paper away from the cake.
Heavily dust the top of the cake with the remaining powdered sugar.
Flip one end of the tea towel over one of the short ends of the cake. Carefully begin to roll one end towards the other. Place the rolled cake on a cooling rack to cool completely.