Whisk the sugar, flour, cocoa, baking soda, baking powder, and salt in a large bowl for 1 minute, until no streaks remain. Press stubborn cocoa lumps against the bowl with a spoon.

Add the eggs, buttermilk, oil, and vanilla, then whisk for 1 minute, until the batter looks smooth and glossy.

Pour in the hot coffee while whisking for 30 seconds, until the batter pours as thin as heavy cream. Do not add flour.

Pour the batter evenly into the two pans and tap each pan on the counter twice, until the surface looks level.

Bake on the center rack for 30 to 35 minutes, until a toothpick comes out clean or with a few dry crumbs and the top springs back when pressed. Keep the oven door shut for the first 25 minutes.

Cool the layers in the pans for 10 minutes, then turn them onto wire racks and peel off the parchment. Cool 50 more minutes, until the bottoms feel cool to the touch.

Beat the softened butter for 2 minutes, until pale and creamy.

Beat in the cocoa, powdered sugar, milk, vanilla, and salt, starting on low and finishing on medium for 2 minutes, until fluffy and spreadable. Add 1 extra tablespoon of milk if stiff.

Spread about 1 cup of frosting over the first layer to the edges, then top with the second layer, until the stack sits straight.

Frost the top and sides with the remaining frosting, until no cake shows through and the top has soft swirls.

Slice with a sharp knife dipped in hot water and wiped dry between cuts, until each of the 12 slices has clean edges.