Butter three 8-inch round cake pans. Line bottoms with parchment; butter parchment. Dust with cocoa powder; tap out excess. Set aside. Sift cocoa powder into a medium bowl; whisk in boiling water. Set aside to cool.
Sift together flour, baking soda, and salt into a large bowl; set aside. Put butter into the bowl of an electric mixer fitted with the paddle attachment. Mix on low speed until creamy. Gradually mix in sugar until pale and fluffy, 3 to 4 minutes. Add eggs, a bit at a time, mixing well between each addition; mix until well blended. Mix in vanilla.
Whisk milk into reserved cocoa mixture. With mixer on low speed, add flour mixture to butter mixture in 3 batches, alternating with the cocoa mixture.
Divide batter evenly among prepared pans; smooth tops with an offset spatula. Bake, rotating pan halfway through, until a cake tester inserted into centers comes out clean, 35 to 45 minutes. Let cool in pans on wire racks 15 minutes. Turn out cakes onto racks; remove parchment and re-invert. Let cool completely.
Using a serrated knife, trim tops of cakes to make level. Place four strips of parchment paper around perimeter of a serving plate or lazy Susan. Place the first layer on the cake plate. Spread the top of the first layer with 1 1/2 cups of frosting. Place the second layer on top and repeat process with another 1 1/2 cups of frosting. Place the remaining layer on top of the second layer, bottom side up. Spread entire cake with remaining 3 cups frosting.