Preheat your oven to 325 degrees F. Spray a 9-inch x 13-inch baking pan with nonstick cooking spray, line the bottoms with parchment paper, and spray again. Set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda and salt. Set aside.
In a stand mixer fitted with the paddle attachment, beat the butter, oil, and sugars on medium-high speed until pale and fluffy, about 5 minutes.
Lower the speed to medium and add the eggs, one at a time, mixing until each is fully incorporated before adding the next (about 30 seconds). Add the vanilla.
With the mixer on low, add the dry ingredients alternating with the buttermilk mixture into the creamed mixture, starting and ending with the dry ingredients. Mix until just incorporated and remove bowl from stand mixer.
Stir in the bananas.
Carefully smooth the batter with small offset palette knife, and bake until a toothpick or skewer comes out clean, about 35 to 40 minutes.
Let the cake cool completely.