3 3/4 cups cake flour
2 1/2 cups sugar
1 tablespoon plus 2 3/4 teaspoons baking powder
1/2 teaspoon salt
2 1/2 sticks (10 ounces) unsalted butter, at room temperature
1 1/4 cups plus 1/3 cup buttermilk
5 whole eggs
2 egg yolks
2 1/2 teaspoons vanilla extract
1. Preheat the oven to 325°F. 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.
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 2 cups 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.
3. In a smaller bowl, whisk together the whole eggs, egg yolks, vanilla, and the remaining 3/4 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.
4. Bake for 26 to 28 minutes, or until a cake tester or wooden toothpick inserted in the center comes out clean.
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 th elayers easier to handle, wrap them on their boards completely in plastic, so they don’t dry out, and refrigerate them.