Devil's Food Cake with Chocolate Spiderweb

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.