Preheat the oven to 400 degrees F (200 degrees C).
Melt 1/4 cup butter in a 12-inch cast iron skillet over medium-low heat. Stir in brown sugar, pineapple juice, and rum. Cook until sugar is dissolved and mixture is bubbling, about 5 minutes. Remove from heat and place pineapple slices in the skillet in a single layer, covering sugar mixture completely. Set skillet aside.
Melt 1/2 cup butter in small skillet over low heat until butter begins to brown and releases a nutty fragrance, about 5 minutes, being careful to not burn the butter. Remove from heat and let cool for 10 minutes.
Combine gluten-free flour and almond flour in a bowl. Mix in white sugar, baking powder, salt, and cardamom until well combined. Whisk in eggs and cold milk; mix until just combined. Pour in melted butter from the small skillet and stir until batter is mixed thoroughly. Pour batter over pineapple slices in the 12-inch skillet. Use a spatula to smooth out surface and spread evenly.
Bake in the preheated oven until cake begins to bubble around the edges, the top is browned, and a toothpick inserted into the center comes out clean, 30 to 35 minutes. Let cool in the skillet for 10 minutes.
Run a knife around the edge of the cake to loosen it from the skillet. Place a large plate on top of the skillet and flip over, presenting the cake with pineapple slices on top. Garnish with maraschino cherries.
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