Preheat the oven to 350 F. Grease a 9 x 13 inch baking pan with butter or cooking spray. If you plan to unmold the cake, line the bottom of the pan with parchment paper for easy removal.
In a medium bowl, mash the bananas with a fork until smooth. You can use and immersion blender or electric beater to make the job easier. Set bananas aside.
In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and brown and white sugars on medium speed, until fluffy, about 3 minutes.
Beat in the eggs and vanilla until well combined, scraping down the sides of the bowl as need. Beat in the bananas.
Reduce the speed to low. Starting with the dry ingredients, alternate adding the flour mixture and buttermilk in 3 instalments each, being careful to only beat until just incorporated. The batter will be lumpy.
Pour the batter into the prepared pan. Drizzle 1/2 cup of the caramel sauce over the batter and swirl around with a butter knife. Bake in the preheated oven for 35-45 minutes, until a toothpick inserted in the center comes out clean. Set pan on a wire rack to cool completely, about 90 minutes or so.