Preheat your oven to 325 degrees F. Spray two 8" x 3" or three 8" x 2" pans with nonstick cooking spray, line the bottoms with parchment paper, and spray again. Set aside.NOTE: if you only have 8"x2" pans, I would make this into a three layer cake. If you split this recipe just between two 2-inch high pans, it might overflow.
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 butter mixture, starting and ending with the dry ingredients. Mix until just incorporated and remove bowl from stand mixer. Using a large stainless steel whisk, stir/whisk the mashed banana into the mixture--you can use use some strength and blend well, ensuring all of the ingredients are well mixed. (If you don't have a large stainless whisk, you can fold the banana mixture in using a rubber spatula until incorporated.)
Divide the batter evenly between the pans, using a kitchen scale for the best accuracy.
Carefully level the cake batter with a spatula or the back of your sppon, and bake until a toothpick or skewer comes out clean, about 40 to 45 minutes for two 8-inch pans and 30 to 35 minutes for three 8-inch pans.
Let pans cool on wire rack for 10 minutes, then invert cakes onto racks, gently, peeling away parchment rounds. Let cool completely.
When the cakes are completely cooled, level the cake layers if necessary
The cake layers can be made up to a week in advance. If you plan to make it in advance, cover each cake layer with two layers of plastic wrap. When you're ready to frost your cake, take the cake layers out of the freezer an hour before you decorate.