Preheat the oven to 350°F (175°C). Lightly grease a 10×15-inch jelly roll pan and line it with parchment paper, leaving an overhang on the sides for easy removal.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat the softened unsalted butter and granulated sugar together until light and fluffy, about 2-3 minutes.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Mix in the mashed ripe bananas until combined.
Alternately add the dry flour mixture and buttermilk to the banana mixture, beginning and ending with the dry ingredients. Mix just until combined; do not overmix.
Pour the batter evenly into the prepared jelly roll pan and smooth the top with a spatula.
Bake for 18-22 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Using the parchment paper overhang, lift the cake out of the pan and transfer it to a wire rack to cool completely before slicing or rolling.