Rehydrate the cherries in the apple juice and let soak until tender. Drain and chop. Slice the pineapple as thin as possible. Sift together the flour, baking powder and salt, 3 times over parchment paper. In a heavy saucepan, heat 1 cup granulated sugar and cook until amber in color, about 5 minutes. Remove from heat and add 3 tablespoons of the butter. Mix carefully with a wooden spoon. Pour the caramel into a 10-inch cake pan and spread around the bottom. Sprinkle with brown sugar. Line the pan with overlapping pineapple slices, covering the entire pan. In the bowl of a mixer, cream together remaining 3 tablespoons butter and vanilla scrapings with remaining 1/4 cup granulated sugar. Add the eggs, 1 at a time, and mix until fluffy. Add the milk alternating in three additions with the sifted dry ingredients. Fold in the cherries. Transfer to the pineapple lined pan. Bake until a cake tester comes out clean, about 70 minutes. Invert onto a cake plate. While the caramel left in the bottom of the pan is still hot, quickly transfer it to a saucepot over low heat. Add heavy cream and stir to make a sauce. Let thicken and serve with cake.