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Preheat oven to 400 degrees. Butter two 9-inch round cake pans. Whisk together flour, baking powder, and salt. In a separate bowl, combine 3/4 cup sugar, the milk, oil, and egg. Fold into flour mixture.
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Divide batter evenly between prepared pans, and smooth tops. Arrange plums, cut sides up, over batter.
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Combine cinnamon and remaining sugar, and sprinkle over plums. Dot with butter. Bake until tops are dark golden, plums are soft, and a toothpick inserted into center of cakes comes out clean, 30 to 35 minutes. Let cool. (Cakes are best the day you make them; leftover cake is great for breakfast the next day.)
Cook’s Notes
To ensure the fruit retains its shape during baking, use plums that are almost — but not quite — ripe. They shouldn’t be rock hard; rather, they should be soft yet slightly firm. You can use apricots, nectarines, or peaches in place of the plums.