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Special equipment:
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A 10-inch cast-iron skillet.
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If you dont have one you can make the caramel in a small pot and scrape it into the bottom of a similarly-sized cake pan.
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Preheat oven to 350F (180C).
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Make topping:
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Cut pineapple crosswise into 38 inch-thick pieces.
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Melt butter in skillet.
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Add brown sugar and simmer over moderate heat, stirring, four minutes.
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Remove from heat.
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Arrange pineapple on top of sugar mixture in concentric circles, overlapping pieces slightly.
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Make batter:
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Sift together flour, baking powder, and salt.
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Beat butter in a large bowl with an electric mixer until light and fluffy, then gradually beat in granulated sugar.
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Add eggs, one at a time, beating well after each addition.
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Beat in vanilla and rum.
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Add half of flour mixture and beat on low speed just until blended.
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Beat in pineapple juice, then add remaining flour mixture, beating just until blended.
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(Batter may appear slightly curdled.)
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Spoon batter over pineapple topping and spread evenly.
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Bake cake in middle of oven until golden and a tester comes out clean, about 45 minutes.
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Let cake stand in skillet five minutes.
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Invert a plate over skillet and invert cake onto plate (keeping plate and skillet firmly pressed together).
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Replace any pineapple stuck to bottom of skillet.
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Sprinkle rum over cake and cool on plate on a rack.
