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1
Preheat the oven to 350F, with racks in the upper and lower thirds.
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2
Cut 2 9-inch rounds of parchment paper to line the bottoms of 2 9-inch (2 inches deep) round cake pans.
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3
Butter and line the pans.
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4
Butter the linings.
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5
Dust the pans with flour, tapping out excess.
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6
Set aside.
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7
Sift together the flour, sugar, baking soda, baking powder, and salt into the bowl of an electric mixer.
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8
Return the bowl to the mixer; fit the mixer with the paddle attachment.
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9
Add the eggs, yolk, warm water, buttermilk, oil, and vanilla.
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10
Mix on low speed until the mixture is smooth, about 3 minutes.
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11
Divide the batter evenly between the prepared pans.
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12
Bake, switching the positions of the pans and rotating them halfway through, until a cake tester inserted into the centers comes out clean, about 42 minutes.
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13
Let cool in the pans on wire racks 30 minutes.
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14
Run a thin knife around the edges of the cakes to loosen.
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15
Unmold; peel off the parchment.
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16
Let cool completely, top sides up, on the racks.
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17
Trim the tops of the cake layers with a long serrated knife to make them level.
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18
Using a small offset spatula, evenly cover the top of one cake layer with 1 1/2 cups frosting; spread the frosting so it extends just beyond the edges of the cake.
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19
Place the second cake layer, cut side down, on top; press gently to make it level.
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20
Frost the top and sides of assembled cake with the remaining frosting.
