Heat the oven to 350°F (175°C). Grease three 9-inch round cake pans and line the bottoms with parchment paper, making sure the pans are leak-free because the batter will be unusually thin.

Whisk the flour, sugar, cocoa powder, baking powder, baking soda, and salt together in a large bowl. Break up any cocoa lumps so the dry ingredients distribute evenly through the batter.

Add the room-temperature eggs, buttermilk, oil, and vanilla extract. Beat for about 1 to 2 minutes, just until the mixture is smooth and evenly combined.

Gradually pour in the hot, strongly brewed coffee while mixing carefully. The batter will become very thin, which is normal and helps produce a moist, tender cake.

Divide the batter evenly among the three prepared pans. Pour slowly and check that each pan contains a similar amount for evenly sized layers.

Bake for 30 to 35 minutes, rotating the pans once if necessary for even baking. The cakes are ready when a toothpick inserted in the center comes out with a few moist crumbs.

Cool the cakes in their pans for about 10 minutes, then turn them out onto wire racks. Let them cool completely before frosting, or chill them for 20 to 30 minutes after cooling for especially clean assembly.

Make the buttercream by beating the softened butter until smooth. Gradually add the cocoa powder, confectioners' sugar, milk, vanilla, and salt, then beat until light and creamy, adding a little more milk if the frosting is too stiff.

Place one cake layer on a serving plate and spread it with buttercream. Add the second and third layers with frosting between each one, then frost the top and sides.