Preheat the oven to 350 degrees F.

Line the base of two 8 inch cake pans or three 6 inch baking pans with wax paper and spray with non-stick baking spray.

Add the flour, sugar, cocoa, baking soda, baking powder, and salt into the bowl of an electric mixer fitted with a paddle attachment and mix on low speed until combined.

In another bowl, combine the milk, vinegar, oil, eggs, and vanilla.

With the mixer on low speed, slowly add the wet ingredients to the dry.

With mixer still on low, add the coffee and stir just to combine, scraping the bottom of the bowl with a rubber spatula.

Pour the batter into the prepared pans and bake for 35 to 40 minutes, until a toothpick comes out clean. Cool in the pans for 30 minutes, then turn them out onto a cooling rack and allow to cool.

Chop the chocolate and place it in a heat-proof bowl set over a pot of simmering water. Stir until just melted and set aside until cooled to room temperature.

In the bowl of an electric mixer fitted with a paddle attachment, beat the butter on medium-high speed until light yellow and fluffy, about 3 minutes.

Add the egg yolk and vanilla and continue beating for 3 minutes.

Turn the mixer to low, gradually add the confectioners' sugar, then beat at medium speed, scraping down the bowl as necessary, until smooth and creamy.

Dissolve the coffee powder in 2 teaspoons of hot water

On low speed, add the coffee to the butter mixture and mix until blended.

Gently fold butter and icing sugar mixture until evenly combined.

Place 1 layer, flat side up, on a flat plate or cake pedestal.

With a knife or offset spatula, spread the top with frosting.

Place the second layer on top, rounded side up, and spread the frosting evenly on the top and sides of the cake.

Add chocolate shaving to top of cake.