Preheat oven to 350 degrees and place rack in center. Butter two 8-by-2-inch round cake pans. Line with parchment paper. Butter the parchment, and dust with cocoa powder, tapping out excess. Sift cocoa over a medium bowl; whisk in boiling coffee and milk. Let cool; set aside. Sift together flour, baking soda, and salt into another medium bowl; set aside.
In a large bowl, mix butter using a rubber spatula until light and fluffy, about 2 minutes. Gradually add sugar and vanilla. Add eggs one at a time, stirring well after each addition. Pour in cooled cocoa mixture. Mix until fully incorporated.
Add flour mixture to chocolate mixture, stirring until just combined. Pour batter into prepared pans (about 4 cups in each pan). Bake for 20 minutes, rotate pans, and bake until a cake tester comes out clean when inserted into center of cake, 20 to 25 minutes.
Remove cakes from oven, and transfer to a cooling rack. Allow to cool in pans for 15 minutes. Carefully run a small offset spatula around edge of cakes to loosen from pan. Invert cakes onto a wire rack. Let cook completely, about 1 hour.
To assemble, using a serrated knife, level the top surface of each cake layer. Place four strips of parchment paper around the perimeter of the lazy susan. Place the first layer on the lazy susan. Spread with 3/4 cup buttercream. Top with the remaining layer, bottom-side up. Spread a thin layer of buttercream on the top and sides of cake, called a crumb coat. Chill until the buttercream is set, at least 30 minutes.
Apply the final coat of buttercream. Smooth the sides with a bench scraper or large offset spatula held steady at a 45-degree angle while turning the lazy susan.