Preheat your oven to 325 degrees F. Spray three 8-inch pans 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. 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. (For this recipe, you'll have about 20 ounces of batter in each of the three 8-inch pans).
Carefully smooth the batter with small offset palette knife, and bake until a toothpick or skewer comes out clean, about 30 to 35 minutes.
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. Using a fork, poke holes all over the cake layers. Drizzle about 1/4 to 1/3 cup of caramel over all three cake layers and allow the caramel to soak in.