Preheat oven to 350°F/175°C. In a large bowl, mash the ripe bananas. Add the eggs, oil, sugar, and cinnamon, mixing until evenly incorporated. Add the flour and mix until the batter has no large pockets of flour. Set aside. In a pot over low heat, melt the butter, then mix in the brown sugar until dissolved. Bring up the heat to medium, cooking until the mixture starts bubbling. Remove the caramel from heat and pour into a greased 9×9 baking pan. Lay the banana slices evenly on top of the caramel. Spread the banana bread batter on top. Bake 40-50 minutes. Cool until the bottom is barely warm and use a knife to loosen the edges from the pan. Place a plate upside-down on top of the pan, then invert the pan, flipping the banana bread onto the plate. Slice, then serve with vanilla ice cream.