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1
Preheat oven to 350F.
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2
Butter 3 (8- by 2-inch) round cake pans and line bottoms of each with rounds of wax or parchment paper.
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3
Butter paper and dust pans with flour, knocking out excess.
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4
Whisk together boiling water and cocoa powder in a bowl until smooth, then whisk in milk and vanilla.
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5
3Sift together flour, baking soda, and salt in another bowl.
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6
Beat together butter and sugars in a large bowl with an electric mixer until pale and fluffy, then add eggs 1 at a time, beating well after each addition.
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7
Beat in flour and cocoa mixtures alternately in batches, beginning and ending with flour mixture (batter may look curdled).
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8
Divide batter among pans, smoothing tops.
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9
Bake in upper and lower thirds of oven, switching position of pans halfway through baking, until a tester comes out clean and layers begin to pull away from sides of pans, 20 to 25 minutes total.
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10
Cool layers in pans on racks 10 minutes, then invert onto racks, remove wax paper, and cool completely.
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11
Put 1 cake layer, rounded side up, on a cake plate and spread with about 1 cup buttercream.
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12
Top with another cake layer, rounded side up, and spread with another cup buttercream.
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13
Top with remaining cake layer and frost top and sides of cake with remaining buttercream.
