1cupplus 2 tablespoons (7 ounces) dark brown sugar
2/3cup(5.3 fluid ounces) vegetable oil
1/3cup(2.65 fluid ounces) whole buttermilk
1teaspoonpure vanilla extract
1 1/2tablespoonsdemerara (or other coarse) sugar
Center a rack in the oven and preheat to 355 (F). Prepare two 9 by 5-inch loaf pans (or one 12 x 5-inch loaf pan by spraying generously with cooking spray. Set aside.
Reserve a lengthwise half of a banana. Place the rest of the bananas in a medium bowl and use your hands to break them up into smaller chunks. Use a fork or a potato masher to mash these banana chunks until you have a chunky mixture. Set aside.
In another medium bowl, combine 1 1/2 cups all-purpose flour, 1 teaspoon baking powder, 1 teaspoon baking soda, and 1/2 teaspoon kosher salt. Whisk together until the ingredients are fully combined. Set aside.
In the bowl of a freestanding electric mixer fitted with a paddle attachment, combine 1 cup plus 2 tablespoons dark brown sugar and 2 large eggs. Beat on medium speed for around 2 minutes, until fluffy. Lower the mixer speed to its slowest setting and add 2/3 cup vegetable oil, 1/3 cup buttermilk, 1 teaspoon pure vanilla extract, and 1 teaspoon dark rum. Beat on medium-low speed for around 2 minutes, until well combined. Lower the mixer back to its lowest setting and add the mashed bananas (from the 2nd step). When all the bananas have been added, sprinkle the dry ingredients (from the 3rd step) over the mixture and beat on the mixer's slowest setting until just combined. At this point, it's okay to stop the mixer even if you still have one or two flour streaks left — you can finish mixing these in by hand, with a rubber spatula. Be careful not to overmix, or you'll end up with a dense, heavy cake and it'll be the worst!
Transfer the batter into the prepared loaf pan. Smooth the top of the batter with an offset spatula and place the reserved banana half on top. Sprinkle the banana and the rest of the cake top with the remaining 1 1/2 tablespoon of demerara sugar.
Transfer to the preheated oven and bake for 50 to 60 minutes, or until a cake skewer inserted into the center of the cake comes out clean, with minimal crumbs. Once the loaf is done, transfer to a wire rack to cool completely in its cake pan.