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for cake:
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1. Preheat the oven to 325u00b0F. Butter and flour three 9-inch round cake pans, put a parchment round in the bottom of each pan, and butter and flour the rounds.
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2. On medium speed, beat the cold butter in the bowl of an electric stand mixer fitted with the paddle attachment, until it is very light, about 5 minutes. Continue beating while gradually adding the sugar, scraping down the sides of the bowl as necessary.
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3. Add the vanilla and beat for 5 more minutes, scraping down the sides of the bowl again. The mixture will be very coarse and grainy. Turn the mixer to the lowest speed, add the melted butter, egg yolks, and whole eggs, and then turn off the mixer.
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4. In a large bowl, sift together the flour, salt, and baking powder.
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5. In another bowl, mix together the buttermilk and cream.
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6. With the mixer on the lowest speed, add half the flour mixture, and then half the buttermilk mixture. Add the remainder of the flour and buttermilk mixtures, scraping down the sides of the bowl as necessary. Do not overmix or the cake will be tough.
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7. Pour the batter evenly into the prepared pans, tapping each pan on a sturdy surface to release air bubbles if there are any, and bake for 25 to 30 minutes until a toothpick or knife comes out clean.
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8. Cool the cakes for 10 minutes, then run the dull edge of a knife around their perimeters and invert them onto a cold baking sheet or rack. (Note: These cakes may be frozen for up to 3 months.)
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9. When you are ready to ice the cake, slice each layer in half horizontally so that you have 6 layers.
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10. To make the glaze, whisk together the powdered sugar and coconut milk in a small bowl. Pierce each cake layer with a fork in several places and then spoon or brush the glaze over them before icing.
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11. Make sure all the layers are completely cool before icing.
