Prepare oven and pan: Preheat the oven to 350 F degrees and grease a 9x13-inch cake pan.
Make the topping: Heat the butter, salt, brown sugar, and vanilla in a skillet on the stovetop. Stir until the brown sugar has dissolved into the butter and the mixture bubbles. Remove from the heat and whisk in the rum. Spread the caramel evenly on the bottom of the greased cake pan, then top with sliced bananas.
Make the cake batter: In a small bowl whisk the flour, baking powder, salt, and cinnamon together. In a separate bowl, mash the ripe bananas using either a fork or a potato masher. Set aside.
In a stand mixer fitted with the paddle attachment, or a mixing bowl using a whisk, beat the butter with the sugar until light and fluffy. Add the eggs one at a time, making sure to scrape down the sides of the bowl between eggs. Stir in the bananas. Mix in half the dry ingredients, the milk and vanilla, and finally the remaining dry ingredients.
Bake the cake: Pour the cake batter over the caramel and banana slices and spread evenly using a spatula. Bake for 30-35 minutes.
Flip the cake: Let the cake cool for 10 minutes. Run a knife along the edges of the cake pan to release the sides.Turn the cake out onto a platter, cooling rack, or a cutting board. Wear oven mitts to protect your hands from hot caramel. Spoon excess caramel back over the cake, serve, and enjoy!