PreparationMake cake: Preheat oven to 350°F with racks in upper and lower thirds. Butter cake pans, then line bottoms with rounds of parchment paper. Dust pans with flour, knocking out excess. Whisk together flour, baking soda, and salt in a small bowl. Whisk together boiling-hot water and cocoa in another bowl until smooth, then whisk in milk and vanilla. Beat butter and sugars with an electric mixer at medium-high speed until light and fluffy, about 3 minutes. Add eggs 1 at a time, beating well after each addition. At low speed, mix in flour mixture in 3 batches, alternating with cocoa mixture, beginning and ending with flour, and mixing until just combined. Divide batter among pans, smoothing tops. Bake, switching position of pans halfway through, until a wooden pick inserted into center comes out clean and cakes begin to pull away from sides of pans, 20 to 25 minutes. Cool cakes in pans on racks 20 minutes, then turn out onto racks to cool completely. Make decorations while cake layers cool: Trace a 9-inch circle on a sheet of parchment paper, then draw a spiderweb inside circle. Next to web, draw a 2-to 3-inch spider. Turn drawings over onto a baking sheet. Melt chocolate chips in a heatproof bowl set over a saucepan of simmering water, stirring. Cool slightly, then transfer to pastry bag. Pipe chocolate onto web, beginning with spokes, and onto spider on parchment, then freeze until firm, about 1 hour. Make frosting: Put frosting ingredients in a heatproof large bowl set over a pot of simmering water. Beat with handheld mixer at low speed until mixture is warm and sugar has dissolved. Continue to beat at high speed until thick and fluffy, 7 to 10 minutes. Remove bowl from heat and beat frosting until cooled slightly, 5 to 10 minutes more. Assemble cake: Place a cake layer on a serving plate. Spread top with some of frosting. Top with another cake layer and spread with some of frosting, then top with final cake layer. Frost top and sides of cake with remaining frosting. Cut off portion of parchment with spider and reserve. Invert web on parchment onto cake and carefully peel off paper. Peel off parchment from spider and put spider on web. Let cake stand at room temperature until chocolate decorations have softened. Cooks' notes:•Cake layers can be made 2 days ahead and kept, well wrapped in plastic wrap, at room temperature, or 1 week ahead and frozen. •Chocolate decorations can be made 1 day ahead and frozen. •You can substitute 2 teaspoons pure vanilla extract for the espresso powder in the frosting. •The egg whites in the frosting may not be fully cooked. •Cake can be assembled and decorated 4 hours ahead and chilled. Let stand at room temperature at least 30 minutes before serving.
PreparationMake cake: Preheat oven to 350°F with racks in upper and lower thirds. Butter cake pans, then line bottoms with rounds of parchment paper. Dust pans with flour, knocking out excess. Whisk together flour, baking soda, and salt in a small bowl. Whisk together boiling-hot water and cocoa in another bowl until smooth, then whisk in milk and vanilla. Beat butter and sugars with an electric mixer at medium-high speed until light and fluffy, about 3 minutes. Add eggs 1 at a time, beating well after each addition. At low speed, mix in flour mixture in 3 batches, alternating with cocoa mixture, beginning and ending with flour, and mixing until just combined. Divide batter among pans, smoothing tops. Bake, switching position of pans halfway through, until a wooden pick inserted into center comes out clean and cakes begin to pull away from sides of pans, 20 to 25 minutes. Cool cakes in pans on racks 20 minutes, then turn out onto racks to cool completely. Make decorations while cake layers cool: Trace a 9-inch circle on a sheet of parchment paper, then draw a spiderweb inside circle. Next to web, draw a 2-to 3-inch spider. Turn drawings over onto a baking sheet. Melt chocolate chips in a heatproof bowl set over a saucepan of simmering water, stirring. Cool slightly, then transfer to pastry bag. Pipe chocolate onto web, beginning with spokes, and onto spider on parchment, then freeze until firm, about 1 hour. Make frosting: Put frosting ingredients in a heatproof large bowl set over a pot of simmering water. Beat with handheld mixer at low speed until mixture is warm and sugar has dissolved. Continue to beat at high speed until thick and fluffy, 7 to 10 minutes. Remove bowl from heat and beat frosting until cooled slightly, 5 to 10 minutes more. Assemble cake: Place a cake layer on a serving plate. Spread top with some of frosting. Top with another cake layer and spread with some of frosting, then top with final cake layer. Frost top and sides of cake with remaining frosting. Cut off portion of parchment with spider and reserve. Invert web on parchment onto cake and carefully peel off paper. Peel off parchment from spider and put spider on web. Let cake stand at room temperature until chocolate decorations have softened. Cooks' notes:•Cake layers can be made 2 days ahead and kept, well wrapped in plastic wrap, at room temperature, or 1 week ahead and frozen. •Chocolate decorations can be made 1 day ahead and frozen. •You can substitute 2 teaspoons pure vanilla extract for the espresso powder in the frosting. •The egg whites in the frosting may not be fully cooked. •Cake can be assembled and decorated 4 hours ahead and chilled. Let stand at room temperature at least 30 minutes before serving.