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Preheat the oven to 350°F. Lightly grease a 9" cast iron skillet (it should measure 9" across the bottom; the top diameter may be greater than 9"). Or lightly grease a 9" x 2"-deep square cake pan.
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Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Whisk together the flour, baking powder, and salt. Set the mixture aside.
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Whisk the egg yolks to combine; set them aside. Beat the whites, separately, until light and frothy.
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Beat the butter until soft and smooth. Gradually beat in the sugar.
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Add the egg yolks, beating to combine. Scrape the bottom and sides of the bowl, and beat again, until smooth.
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Add the milk alternately with the flour mixture, mixing gently but thoroughly after each addition.
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Fold in the beaten whites, then the vanilla.
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To make the topping, melt the butter in the skillet, and sprinkle the sugar evenly on top. Space pineapple rings atop the sugar.
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Spoon the batter on top.
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Bake the cake for 35 to 45 minutes, until a toothpick inserted into the center comes out clean.
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Remove the cake from the oven. Loosen its edges. CAREFULLY turn the cake upside-down onto a serving plate. Lift the pan off the cake, scraping any pineapple or brown sugar from the pan onto the cake, if it sticks.
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Place the cherries artfully atop the warm cake, pressing them in gently.
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Serve the cake warm, or at room temperature. Store it at room temperature, well-wrapped, for several days; freeze for longer storage.
