Fresh fruit gives a lift to this favorite from the 1920s, when supersweet canned pineapple and Maraschino cherries were chic. Use a juicy, ripe pineapple that yields to thumb pressure and that has a sweet perfume.
Using a sharp knife, peel the pineapple and remove the eyes. Halve the pineapple lengthwise and cut out the center core. Cut each half crosswise into five 2/3-inch-thick semicircles. Cut one of the semicircles into 3 pieces.
Preheat the oven to 375°. In a small bowl, stir together the flour and baking powder. In a medium bowl, beat 1 stick of the butter until pale and creamy. Gradually beat the granulated sugar into the butter until the mixture is fluffy. Beat in the eggs one at a time, beating well after each addition. Stir in the flour mixture in 3 batches just until smooth. Stir in the Cognac and set aside.
Melt the remaining 3 tablespoons butter in a 9-inch cast-iron skillet; if the handle isn't ovenproof, wrap it in foil. Stir in the brown sugar and cook over moderate heat until melted and bubbling, about 3 minutes. Remove the pan from the heat. Arrange the 9 pineapple semicircles in a tight concentric ring in the skillet and fit the 3 small pieces in the center. Cook over moderately high heat for 10 minutes. Turn the pineapple slices and lower the heat so that the mixture simmer vigorously. Cook until the fruit is tender when pierced, about 10 minutes longer. Insert a cherry in the hollow of each semicircle.
Remove the skillet from the heat and spread the cake batter evenly over the hot pineapple; it may not completely cover the fruit, but it will spread as it cooks. Bake in the middle of the oven for about 20 minutes, or until the cake springs back when pressed. Let it cool for 10 minutes, then invert the cake onto a large platter. Serve the cake warm with vanilla ice cream.