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1. Preheat the oven to 325u00b0F Butter three 9-inch round cake pans. Line the bottom of each pan with a round of parchment or waxed paper and butter the paper.
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2. Combine the cake flour, sugar, baking powder, and salt in a large mixer bowl. With the mixer on low speed, blend for 30 seconds. Add the butter and 1 1/4 cup of the buttermilk. Mix on low speed briefly to blend; then raise the speed to medium and beat until light and fluffy, 2 to 3 minutes.
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3. In a smaller bowl, whisk together the whole eggs, egg yolks, vanilla, and the remaining 1/3 cup buttermilk until well blended. Pour one-third of the egg mixture into the cake batter at a time, folding it in completely after each addition. There will be 9 cups of batter; our 3 cups batter into each pan.
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4. Bake for 26 to 28 minutes, or until a cake tester or wooden toothpick inserted in the center comes out clean.
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5. Turn the layers out onto wire racks by placing a rack on top of a pan, inverting it, and lifting off the pan. Peel off the paper liners and let cool completely. When the layers have cooled, place a cardboard cake board on top of a layer, invert again, and lift off the rack. To make the layers easier to handle, wrap them on their boards completely in plastic, so they don't dry out, and refrigerate them.
