Preheat the oven to 350℉. Butter two 8-inch round cake pans. Line with parchment paper, then butter and flour the pans.

Sift the flour, sugar, cocoa, baking soda, baking powder, and salt into the bowl of an electric mixer fitted with the paddle attachment. Or, if using a hand mixer, into a large bowl. Mix on low speed until well combined.

In another bowl, combine the buttermilk, oil, eggs, and vanilla. With the mixer on low speed, slowly add the wet ingredients to the dry ones. 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 evenly into the prepared pans and bake for 35 to 40 minutes, until a cake tester comes out clean. Cool in the pans for 30 minutes, then turn them out onto a cooling rack and cool completely. It's normal for the top of the cake to sink a little in the center.

Place the heavy cream in the bowl of a stand mixer or a large bowl, if using a handheld electric mixer. Fitted with the whisk attachment, beat for about 5 minutes or until medium-stiff peaks form. Be careful not to overbeat otherwise it can turn into butter. Transfer the whipped cream to another bowl and set aside.

In the emptied bowl, add the cream cheese and sift the confectioner sugar on top of it. Beat with the paddle attachment for 3 to 5 minutes, until thick and smooth. Carefully add the whipped cream to the cream cheese mixture, a small amount at a time, mixing on low speed or fold with a spatula just until combined. Gently mix in the vanilla just until blended. 

Refrigerate the filling for at least 30 minutes for best spreading consistency for a cake. Can be prepared ahead of time and stored in the fridge until needed.

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

Beat the butter in the bowl of an electric mixer fitted with the paddle attachment on medium-high speed until light yellow and fluffy, about 3 minutes. Alternatively, a hand held mixer can be used. Add the egg yolk and vanilla and continue beating for 3 minutes. Turn the mixer to low, gradually add the sifted confectioners’ sugar, then beat at medium speed, scraping down the bowl as necessary, until smooth and creamy.

Dissolve the espresso powder in 2 teaspoons of the hottest tap water. On low speed, add the cooled chocolate and the coffee to the butter mixture. Mix until blended. Don’t whip! It's ready to spread on the assembled cake.

Note: You can use either bittersweet or semisweet chocolate but don’t use chocolate chips because they have stabilizers in them.

Melt chocolate with the butter in a heatproof bowl set over a pan of simmering water, stirring occasionally. Pour the melted chocolate onto a large rimmed baking sheet. Smooth with an offset spatula. Refrigerate until chocolate is set but not brittle, about ten minutes.

Holding a sturdy metal spatula or a bench scraper at a 45° angle, scrape chocolate away from you to form curls. If chocolate is too brittle, let stand at room temperature for 1 to 2 minutes before trying again. If too soft, refrigerate briefly. Break each curl into 1-inch pieces. Curls can be made ahead and refrigerated in an airtight container for up to 2 weeks.

Insert toothpicks around the perimeter of each cake carefully placed halfway up all around. Using a very sharp large knife, use the toothpicks as your guide and cut each cake in half horizontally. You now have four layers.

Using a pastry brush, gently remove any excess crumbs. Remove and discard the toothpicks. Choose your cake plate or stand. Cut four strips of parchment paper and place them around the edges of the plate. This will minimize the amount of overflow icing and crumbs that will end up on your serving dish. Then place just a dab of prepared filling to the center of the plate so that the cake will be less likely to shift as you assemble it.

It is easier to spread the cheesecake filling on each layer if it has been placed cut-side-down on the plate. Way less crumbs that way. Spread a generous amount of the cheesecake filling from the center out to the edges where you may need a little extra to fill in any gaps. Carefully place the next layer on top and repeat for the next two layers.

Once the stack is complete, spread the chocolate frosting evenly first on the sides and then on the top of the cake. If you plan to add some decorative piping, don't apply too much frosting on the top and sides. That way, you'll have a small amount left for decorating the cake.

If desired, scoop any remaining frosting into a pastry bag. Using a star tip, or one of your choice, pipe a distinctive design around the entire top edge of the frosted cake. Sprinkle with sugar crystals or sprinkles. If using chocolate curls, scatter them in a generous layer to cover the entire cake top within the decorative piping. Cut in wedges and serve at room temperature. Store any leftover cake in the refrigerator for up to five days.