Preheat the oven to 350 degrees F.
In a 10-inch cast iron skillet, melt the butter over medium heat. Mix in the brown sugar and salt and stir until the sugar begins to bubble, about 1 minute. Pour in the dark rum and bring to a simmer for about 1 to 2 minutes; we just want to burn off a bit of the alcohol. Turn off the heat and allow to cool slightly. Next, arrange the slices of banana to your liking.
In a medium bowl, mix together the flour, baking powder and salt. Next, in the bowl of a stand-up mixer, with the paddle attachment, cream together the butter and sugar until light and fluffy, about 1 minute. Add the eggs and vanilla; and then mix until the mixture. It might look a bit curdled but that’s ok—it’ll come together.
To the butter and sugar mixture, mix in half of the flour mixture and the milk. Then, mix in the remaining flour mixture, being sure not to over mix.
Pour the batter over the bananas, and spread the batter gently so it’s nice and even and reaches the edges of the pan. Transfer the cast iron skillet to the oven and bake for 40 to 45 minutes or until a skewer comes out clean and the top is nice and lightly golden brown.
Remove the cake from the oven and allow to cool for 5-10 minutes. To invert the cake, place a (large enough) plate on top of the cast iron skillet and turn both of them over—be careful, it’ll be heavy. Lift up the cast iron skillet and voila! Your cake! Serve with a side of whipped cream and a cafecito!