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Preheat the oven to 350°F. Lightly grease a 9" cake pan with non-stick baking spray or shortening.
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To make the sauce: In a medium (2- to 3-quart) saucepan, melt the butter and whisk in the brown sugar and pineapple juice until well blended.
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Cook over low heat until the sugar is completely dissolved. Increase the heat and boil until the mixture thickens a little, and the temperature reaches 235°F to 240°F (soft-ball stage). Depending on pan size, this will take between 3 and 5 minutes. If you don't have a thermometer, drop a bit of the syrup into a glass of cold water; it will form a soft, flexible ball when it's reached the proper temperature.
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Pour the sauce into the prepared pan. Set your saucepan aside; don't wash it, you'll be using it again.
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Arrange the drained pineapple slices in the pan. Place a maraschino cherry into the middle of each pineapple slice. Set aside.
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Place the butter for the cake into the saucepan. Swirl the butter around to melt it, and mix in any remaining sugar syrup; don't worry if it has some lumps.
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Whisk in the sugar and vanilla.
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Add the eggs one at a time, whisking well after each addition.
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Add the flour and pineapple juice to the mixture. Whisk until fairly smooth.
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Pour the batter into the prepared pan.
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Bake the cake for 35 to 40 minutes, until evenly browned and a cake tester inserted into the middle comes out clean.
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Remove the cake from the oven, and cool it in the pan for 10 minutes. Run a spatula around the edges to loosen, and turn it out onto a serving plate. Serve warm, or at room temperature, with whipped cream or ice cream, if desired.
