Preheat your oven to 325 degrees F. Spray an 8x8 square inch cake pan with cooking spray, line with parchment paper, and spray again. Set aside.
In a medium bowl, whisk the flour, baking powder, baking soda and salt. Set aside.
In another medium sized bowl, mash the bananas with a fork until they are completely mashed.
In a stand mixer fitted with the paddle attachment, cream the butter, oil, and sugar on medium-high speed until light and fluffy, about 5 minutes. With a rubber spatula, scrape down the sides and bottom of the bowl.
Turn the mixer speed down to medium, and add the eggs, one at a time, mixing until each is fully incorporated before adding the next (about 30 seconds for each addition). Add the vanilla and banana extract (if adding) and mix on low.
With the mixer on low, add half of the dry ingredients, and half of the buttermilk, add the rest of the buttermilk and dry ingredients. Mix until just incorporated and remove bowl from stand mixer.
With a rubber spatula, fold in the mashed bananas until just incorporated. Make sure to scrape down the bottom of the bowl.
Add the the batter to the prepped pan, and carefully smooth the batter with a small offset spatula and bake until a toothpick comes out clean, or with only a few crumbs on it, about 35-40 minutes. Depending on your oven.
Let the cake cool for roughly 10 minutes, then transfer the cake out of the pan and onto a cooling rack. Let the cake cool completely. While the cake is cooling, make the frosting.
For the cream cheese buttercream
In the bowl of an electric mixer, combine the butter and cream cheese. Beat on medium speed for about 2 minutes. Scrape down the sides and bottom of the bowl. Beat again for 2 more minutes.
With the mixer on low, add the powdered sugar, followed by the cream, vanilla extract, vanilla bean paste, and a pinch of salt. Beat on low just until combined. With a rubber spatula, scrape down the sides of the bowl.
Turn the mixer up to medium speed and beat for about 3 to 5 minutes.
With a rubber spatula or a wooden spoon, beat out all of the air pockets by hand for a smooth look.
When the cake is cooled, use an offset spatula and frost the top of the cake. This cake is good served at room temperature or cold. However you serve it, it will not disappoint!