Melt 4 tablespoons of the butter in a 10-inch cast iron skillet, over medium heat. Add the brown sugar and stir to combine. Increase the heat to medium high and cook until the sugar mixture is bubbly, about 2 minutes. Arrange pineapple slices in the skillet in a pleasing pattern and continue to cook for 2 minutes, or until the sugar mixture turns an amber color. Turn the pineapple slices over and remove the pan from the heat. (The mixture will continue to cook even though the heat is off.) Arrange the pecan halves in the spaces between the rings. Set aside to cool slightly.

Preheat the oven to 375 degrees F.

Stir together the flours, baking powder, baking soda, and salt in a medium mixing bowl.

In the bowl of an electric mixer, cream together the remaining 1/2 cup butter and the granulated sugar until light and fluffy. Add the eggs, 1 at a time, mixing just until incorporated. Add the flour mixture and buttermilk alternately in 3 batches, mixing at low speed after each addition until just combined. Stir in the vanilla and rum.

Spoon the batter evenly over the pineapple slices in the skillet. Bake in the middle of the oven until golden brown and a tester comes out clean, 35 to 40 minutes.

Cool the cake in the skillet on a wire rack for 4 minutes only. Run a thin knife around the edge of the cake and, wearing oven mitts and working quickly, invert the cake onto a cake plate, keeping plate and skillet firmly pressed together. Carefully lift the skillet off cake and replace any fruit stuck to the bottom of the skillet, if necessary. Arrange the fresh cherry halves, cut side down, into the top of the cake, in the center of the pineapple rings.

Serve cake warm or at room temperature.