Preheat your oven to 325°F (163°C). Spray a 9×13 metal pan with non-stick spray, line the bottom with parchment paper, and spray again. Use metal binder clips to secure the parchment paper. Set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In another medium-sized bowl, mash the bananas with a fork until completely smooth. Set aside.
In a stand mixer fitted with the paddle attachment, beat the butter, oil, and sugar on medium speed until light and fluffy, about 3 minutes. Scrape down the sides of the bowl with a rubber spatula to ensure even mixing.
Add the eggs, one at a time, mixing until each is fully incorporated before adding the next (about 30 seconds per addition). Add the vanilla and mix on low until combined.
With the mixer on low, add the dry ingredients alternately with the buttermilk, beginning and ending with the dry ingredients. Mix until just incorporated, then remove the bowl from the stand mixer.
Fold in the mashed bananas with a rubber spatula until fully incorporated, making sure to scrape down the bottom of the bowl.
Evenly distribute the batter into the prepared cake pan and smooth out the top with the back of a spoon.
Bake for 45-50 minutes, or until a toothpick inserted into the center of the cake comes out with just a few moist crumbs.
Allow the cake to cool completely in the pan before proceeding.
For the Caramel Sauce:
In a medium-sized saucepan, combine the water, granulated sugar, and corn syrup. Gently mix together before turning on the heat.
Over medium heat, bring the sugar mixture to a boil. Bubbles will be fast and small at first, then slow down and become larger as it caramelizes. Do not stir during this process to prevent crystallization.
Let the mixture boil until it turns golden brown. This may take a few minutes, so watch closely to avoid burning.
Heat the cream in the microwave for 1 minute until warm.
Once the caramel achieves a golden brown color, remove it from heat and carefully add the warm cream. Stir until the caramel and cream are thoroughly combined. Be cautious, as the mixture will bubble up.
Transfer the caramel mixture to a separate bowl, then add the vanilla, salt, and butter. Let it sit until the butter melts, then stir until well incorporated.
Allow the caramel to cool completely before using it on the cake.
For the Cream Cheese Frosting:
In the bowl of an electric mixer, combine the room-temperature butter and cream cheese. Beat on medium speed for about 2 minutes. Scrape down the sides and bottom of the bowl, then beat for an additional 2 minutes.
On low speed, add the sifted powdered sugar, followed by the cream, vanilla extract, and a pinch of salt. Beat on low until fully combined. Scrape down the sides of the bowl.
Increase the mixer speed to medium-high and beat for about 3 to 5 minutes until light and fluffy.
Use a rubber spatula or a wooden spoon to remove any air pockets by mixing gently for a smooth consistency.
Assembly:
Leave the cake in the pan. Once it's completely cool, frost the cake with the cream cheese frosting.
Add dollops of caramel sauce to the frosted cake (you'll only need about half of the caramel; serve the remaining half on the side with each slice).
Swirl the caramel into the cream cheese frosting using a knife or a skewer.
Serve the cake at room temperature.
Notes
Make sure all ingredients are at room temperature for the best results.
Do not overmix the batter to keep the cake light and fluffy.
Watch the caramel closely to avoid burning, as it can change from perfect to burnt quickly.
Allow the cake and caramel to cool completely before assembling to prevent the frosting from melting.