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Preheat oven to 350 degrees F.
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For the topping
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Heat 4 T. (55g) butter, brown sugar and vanilla seeds in a 10-inch cast iron skillet on top of your stove.Stir this mixture constantly until the ingredients are well mixed, liquified and beginning to bubble. Take the pan off the heat and stir in the rum and the split vanilla bean.
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Peel the bananas and cut them lengthwise. Then, cut each banana piece into thirds lengthwise. . You will have long slender banana pieces. It is not a problem if some of the banana pieces break, Carefully arrange the banana slices on top of the brown sugar mixture in the skillet.
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For the cake
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Sift the flour into a large bowl and whisk baking powder, salt and cinnamon into the flour. Set this mixture aside.
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Attach your paddle attachment to your stand mixer and beat the butter and the granulated sugar until the mixture is light and fluffy. Add the eggs one at a time, scraping the sides of the bowl between additions.
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Turn your mixer to its slow speed and add half the dry ingredients to the sugar mixture. Add the milk and the vanilla. Add the rest of the dry ingredients. Mix these ingredients only until they are just incorporated. You need to be careful not to overmix or your cake will not be tender.
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Pour the batter into the skilled and on top of the brown sugar and banana mixture you have prepared.
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Bake cake for 30 to 35 minutes. When the cake is done, a toothpick inserted into the middle of the cake will come out clean. Also, the cake should be firm to your touch when it is done.
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Cool cake in the pan on a rack for ten minutes. Then, run a knife around the edge of the cooled cake. Invert the cake over a large serving plate. (Be careful when you do this. You don't want hot caramel on your hands.)