Special equipment: a clean flathead screwdriver, a piping or resealable plastic bag and a large round piping tip (such as a 2A tip)
For the chocolate cake: Preheat the oven to 350 degrees F. Butter two 8-by-2-inch round cake pans. Line the bottom of each pan with parchment paper, then butter and flour the pans.
Sift the flour, sugar, cocoa powder, 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.
Whisk together the buttermilk, oil, vanilla and eggs in a medium bowl. With the mixer on low speed, slowly add the buttermilk mixture to the flour mixture. With the mixer still on low, add the coffee and mix until just combined, scraping the bottom of the bowl with a rubber spatula.
Pour the batter into the prepared pans and bake until a cake tester comes out clean, 35 to 40 minutes. Cool in the pans for 30 minutes, then turn the cakes out onto cooling racks and cool completely.
When the cakes are completely cool, level each cake and then cut each layer in half to make four cake rounds. Chill until ready to assemble.
For the mint buttercream: In the bowl of stand mixer fitted with a paddle attachment, beat together the confectioners' sugar and butter until creamy.
Beat in the peppermint extract, salt and 2 tablespoons of the milk until well combined. Gradually stir in the remaining 2 tablespoons milk until the desired spreading consistency is reached. Set aside until ready to assemble the cake.
For the chocolate buttercream: Chop the chocolate and place in a heatproof bowl set over a pan 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 vanilla and egg yolk and continue beating for 3 minutes. Turn the mixer to low, gradually add the confectioners' sugar, then beat at medium speed until smooth and creamy, scraping down the bowl as necessary.
Dissolve the coffee powder in 2 teaspoons of the hottest tap water. With the mixer on low speed, add the melted chocolate and the coffee to the butter mixture and mix until blended. Do not whip! Set aside until ready to assemble the cake.
For the mint curls: Put the melting wafers and shortening in a large microwave-safe bowl. Heat in the microwave in 1-minute increments, then in 15-second increments, stirring after each heating. When the wafers are melted, add the peppermint oil and stir until incorporated.
Flip over a large, clean baking sheet. Pour half of the melted candy onto the back of the baking sheet and spread evenly with an offset spatula. (This is important, as you want the layer to be as even and level as possible. Thin is good, but translucent is not.)
Place the baking sheet in the fridge to set for 1 to 2 minutes or leave it on the counter for about 10 minutes. The mixture needs to be at the perfect temperature for curls to form. If it's too cold, they will just break. If it's too warm, they will just be blobs. Press your finger into the mixture; if it leaves a mark, the mixture is too soft.
Press a very clean flathead screwdriver into the mixture at a 45-degree angle and then slide it forward slowly. Curls should form. Immediately transfer the curls to a plate and place in the refrigerator so that they hold their shape. Repeat the process with the remaining half of the melted candy. Chill all the mint curls until ready to assemble the cake.
To assemble the cake: Place 1 layer of cake on a cake stand or cake plate. Spread one-third of the mint buttercream over the top of the cake. Top with a second layer of cake and spread another third of the mint buttercream over the top. Repeat with a third layer of cake and the remaining mint buttercream. Top with the remaining layer of cake.
Coat the top and sides of the assembled cake with the chocolate buttercream. Smooth the surfaces of the cake as much as possible. Place the remaining chocolate buttercream into a piping bag or resealable plastic bag fitted with a large round tip, such as a 2A tip.
Pipe dollops of frosting around the top of the cake. Sprinkle the mint curls over the top. Chill the cake until ready to serve.