Preheat oven to 350 degrees F. Spray a baking dish (I used an 8×11 dish) with nonstick spray. In a small bowl, whisk together flour, baking powder, salt and cinnamon. Set aside. In another smaller bowl or using your electric mixer or hand-mixer, beat egg whites until stiff peaks form. Set aside.
In the bowl of your electric mixer, combine egg yolks and sugars. Beat on medium speed until creamy and combined, then add in vanilla extract and bananas. With the mixer on low speed, add in cooled butter and mix until combined. Add in half of the dry ingredients, then add the 2/3 cups of milk. Finish by adding the remaining dry ingredients and mix until just combined. Remove the bowl from the mixer base and using a large spatula, fold the egg whites into the batter. Pour batter in the greased dish. Bake for 25-30 minutes, or until cake is set in the center and slightly golden. [a 9×9 pan may require a little longer bake time;a 9×13 may require a little less – I would start with 20 minutes.] Remove and let cake cool slightly. You can either leave the cake in the dish to cool, or gently turn it over on a rimmed platter. Let it cool completely, then poke a ton of holes in the top with a fork.
In a large measuring cup, whisk together coconut milk, condensed milk and evaporated milk. Pour the milk mixture over the cake, letting it seep into the fork holes. Let set for about 45 minutes.
To make the frosting, add the cold whipping cream to the bowl of your electric mixer and beat until stiff peaks form, about 3-4 minutes. Add in the powdered sugar and beat on medium speed to combine. Spread whipped cream evenly over the top of the cake.
To make the caramelized bananas, heat a saucepan over medium heat. Add butter and one sizzling, toss in bananas, salt, cinnamon and sugar, tossing well to coat. Cook for 4-5 minutes, tossing occasionally, until bananas are golden brown. Remove and let cool slightly. Serve cake with bananas on top or as a garnish. Note: you do want to store this cake in the fridge, but it can get slightly dense because of the bananas. I recommend letting it sit out for 30-60 minutes before serving!