9 (1/2-inch) slices fresh pineapple, from 1 medium pineapple
12 (1 1/2 sticks) tablespoons unsalted butter at room temperature, divided
3/4 cup packed light brown sugar
1 1/2 cups all-purpose flour
2 teaspoons baking powder
1/2 teaspoon salt
1 cup sugar
3 1/2 teaspoons dark rum, divided
1 teaspoon vanilla extract
1/2 cup pineapple juice
Adjust oven rack to middle position and preheat oven to 350°F. Heat 6 tablespoons butter in 10-inch cast iron skillet over medium high heat until melted. Stir in brown sugar and cook until caramelized, about 4 minutes. Remove from heat. Lay pineapple rings in overlapping circles to cover surface of skillet. Set aside.
In a medium bowl, whisk together flour, baking soda, and salt. In a large bowl, cream together remaining 6 tablespoons butter and sugar with a wooden spoon or electric mixer until light and fluffy, about 4 minutes. Beat in eggs one at a time. Beat in vanilla and 1 1/2 tablespoons rum. Add half of dry ingredients into bowl and beat to combine. Add pineapple juice. Add remaining dry ingredients to bowl and beat until just combined.
Pour batter over pineapples and smooth surface with a spatula. Transfer to oven and bake until a cake tester comes out clean, about 40 minutes. Let cake cool for 5 minutes in pan, then invert onto a plate. Sprinkle remaining rum over cake.