Preheat your oven to 350°F.

Line two 9-inch round cake pans with parchment paper and lightly grease the sides.

In a large mixing bowl, whisk together flour, sugar, cocoa powder, baking soda, baking powder, and salt.

In another bowl, whisk together eggs, cooled coffee, buttermilk, oil, and vanilla extract.

Pour the wet ingredients into the dry mixture and fold together with a rubber spatula until just combined.

Divide batter equally between prepared pans and bake for 30 to 35 minutes.

Let cakes cool in the pans for 15 minutes, then turn out onto wire racks to cool completely.

For the fudgy middle layer, melt 1 cup butter over low heat, whisk in 2/3 cup cocoa powder, then stir in powdered sugar, milk, and vanilla until smooth.

For the chocolate frosting, beat 1 1/2 cups softened butter until pale, then add cocoa powder and alternating powdered sugar and milk until light and fluffy.

Assemble the cake by spreading the fudgy middle layer on one cake layer, place the second layer on top, and frost the top and sides with chocolate frosting.

Chill the cake for at least 2 hours before serving.