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1
Prepare the pan: Use a knife to cut around the fruit to remove the peel and pith of the oranges. Slice all of the fruits into 1/2-inch thick slices. Cut each slice into quarters.
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2
Use the butter to generously grease a 9x13-inch baking pan-be especially generous with the bottom and corners of the pan. (It may feel like a lot of butter-even too much-but trust in the goodness of butter! It plays an important role here.) Sprinkle the brown sugar evenly over the base of the pan. Arrange the fruit in an even layer on top of the sugar-pack it quite tightly so that the whole base is evenly covered.
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3
Preheat the oven to 350u00b0F. Make the cake batter: in the bowl of an electric mixer fitted with the paddle attachment, cream the butter, sugar, and brown sugar until light and fluffy, 4 to 5 minutes.
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4
Add the eggs one at a time, mixing until well incorporated, and scraping the bowl after each addition. Add the vanilla extract and mix to combine.
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5
In a medium bowl, whisk the flour, baking powder, baking soda, and salt together to combine. Add about half of the mixture to the mixer and mix to incorporate. Add half of the yogurt, and mix to combine. Repeat until all of the flour mixture and the yogurt are incorporated.
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6
Dollop the batter all over the pan, and use a small offset spatula to spread into an even layer-it should be pretty easy, but take care not to disturb the oranges underneath.
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7
Bake the cake until a toothpick inserted into the center comes out clean, 35 to 40 minutes. Let the cake cool for 15 minutes inside the pan, then run a small offset spatula around the outside edge. Flip the cake onto a cooling rack set on top of a baking sheet (it may have some excess juices that run off). Cool completely, then serve with whipped cream.
