Preheat the oven to 450°F. Line a baking sheet with parchment paper.
Place sugar in a small bowl. Scrape the seeds from the vanilla bean, add to the sugar, and rub them into the sugar with your fingers until evenly dispersed. Transfer 1 teaspoon of the sugar to a separate small bowl and set aside.
In a large bowl whisk to combine 3 tablespoons vanilla sugar, flour, baking powder, and salt. Add cream and mix until combined.
Place 4 big spoonfuls of dough on the baking sheet. Sprinkle with remaining 1 teaspoon vanilla sugar. Bake until lightly browned, about 15 minutes.
While the shortcakes bake, heat a large nonstick skillet over medium heat. Add butter, sugar, and salt and stir until melted and bubbling. Add banana slices to skillet in a single layer and cook, turning once, until caramelized, 3-4 minutes. Take off the heat and sprinkle rum over bananas.
In a large bowl combine cream, sugar, and rum. Beat until cream is softly whipped.
To serve, cut shortcakes in half. Place bottom halves on serving plates. Top with a dollop of whipped cream and a spoonful of bananas. Place other half of shortcakes on top. Serve immediately.