Prep the oven and pan. Position a rack in the center of the oven and preheat the oven to 350°F. Spray an 8-inch square pan with cooking spray and line it with parchment paper. Spray the parchment, too.
Make the fruit topping. In a small sauce pan, combine the butter, brown sugar, and cinnamon for the topping. Cook over medium heat, stirring occasionally, until melted and combined. Remove from the heat and immediately whisk in the rum and vanilla. Pour the mixture into the prepared pan and arrange the fruit on top of the mixture. Mix the dry ingredients for the cake. In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
Whisk the sugar and wet ingredients for the cake. In a large bowl, whisk together the brown sugar, eggs, buttermilk OR sour cream, oil, and vanilla.
Combine the wet and dry ingredients. Gradually whisk the dry ingredients into the wet ingredients until just combined.
Finish assembling the cake. Pour the batter into the prepared pan and use an offset spatula to smooth the top. Bake the cake. Bake for 32 to 35 minutes, or until a skewer inserted into the center of the cake comes out with few crumbs attached.
Invert the cake. Cool the cake in its pan on a wire rack. After 15 minutes, place a serving plate over the cake and flip the entire thing to turn the cake out of its pan and onto the plate. Peel off the parchment paper if necessary. Serve and store. Serve warm, or at room temperature. The upside down cake can be stored at room temperature, wrapped tightly in plastic wrap, for up to 3 days.