Step 1
Preheat the oven to 400 degrees F (200 degrees C).
Step 2
Melt 1/4 cup butter in a 12-inch cast iron skillet over medium-low heat. Stir in brown sugar pineapple juice and dark rum. Cook over medium-low heat until sugar is dissolved and mixture is bubbling about 5 minutes.
Step 3
Remove from heat and spread pineapple slices in a layer over the brown sugar mixture completely covering the mixture. Set skillet aside.
Step 4
Melt 1/2 cup butter in small skillet over low heat until the butter begins to brown and release a nutty fragrance about 5 minutes. Watch carefully butter burns easily. Remove from heat and let cool for 10 minutes.
Step 5
Whisk together flour cardamom salt baking powder and white sugar in a large bowl. Whisk in egg and cold milk until just combined. Pour in melted butter and stir to mix thoroughly.
Step 6
Pour batter over the pineapple slices in the skillet; spread evenly to cover.
Step 7
Bake in preheated oven until the cake begins to bubble around the edges the top is browned and a toothpick inserted into the center comes out clean about 30 to 35 minutes. Let cool in the skillet for 10 minutes.
Step 8
Loosen the cake from the skillet by running a knife around the inside edge of the cake. Invert a large plate over the top of the skillet and flip over releasing the cake to show the pineapple slices on top.