Martha's version of a classic pineapple upside-down cake uses dried tart cherries for maraschinos, and features a layer of thinly sliced fresh pineapple. Serve the cake in generous slices, with a dollop of rum-spiked whipped cream.
Heat oven to 350 degrees. Line a baking sheet with parchment. Place cherries in a small heat-proof bowl. Bring 1 cup water to a boil in a small saucepan. Pour over dried cherries, and soak for 10 minutes. Drain well, and coarsely chop. Using a wide Japanese mandoline, slice whole pineapple as thinly as possible. Set aside. Sift together flour and baking powder. Set aside.
Heat 1/2 cup of granulated sugar in a 10 1/2-inch cast-iron skillet. Cook until deep amber, about 5 minutes. Remove the pan from the heat. Add 4 tablespoons (1/2 stick) butter, stirring vigorously with a wooden spoon. Spread caramel evenly to coat the bottom of the skillet, and sprinkle with dark-brown sugar.
Center one piece of pineapple in the skillet. Place pineapple slices in a tightly overlapping circle. Make a second ring, completely covering the bottom and continuing at least halfway up the sides. Place one remaining slice in the center of the skillet on top of the circles. (Be certain that there are no gaps as the bottom will be the top upon inversion).
In a heavy-duty mixer fitted with the paddle attachment, cream remaining butter, remaining 3/4 cup of granulated sugar, and vanilla-bean scrapings. Add eggs one at a time, mixing well after each addition. Pour in milk and almond extract. Slowly add sifted flour, scraping sides as needed. Using a rubber spatula, fold in chopped cherries. Pour batter into pineapple-lined skillet. Spread batter evenly with an offset spatula.
Place skillet on a prepared baking sheet, and transfer baking sheet to oven. Bake until golden brown and cake tester comes out clean, about 45 minutes.
Meanwhile, pour cream into the bowl of a heavy-duty mixer. Add rum. Whip on high speed until stiff peaks form, 45 to 60 seconds. Remove cake from oven, and pour excess liquid from skillet into a measuring cup. Carefully invert onto large cake plate, and pour reserved liquid over cake. Serve with rum-spiked whipped cream.