To make the chocolate cake, heat the oven to 325º. Butter three 8-inch cake pans, line them with parchment and butter the parchment. Lightly dust the inside of the pans with flour and tap out the excess. In a medium bowl, whisk together the cocoa powder, sour cream and hot water. Set aside to cool. Sift together the flour, baking soda, baking powder and salt into a large bowl and set aside.

Using a stand mixer fitted with the paddle attachment, combine the butter and shortening together on medium speed until light and fluffy, 3-5 minutes. Add the sugars and continue beating until light and fluffy, an additional 3-5 minutes. Add the eggs, one at a time, beating well after each addition. Scrape down the sides and bottom of the bowl as needed. Reduce speed to low and mix in the vanilla.

Add the flour mixture and cocoa mixture to the bowl in three alternating parts, beginning and ending with the dry ingredients. Mix until just incorporated. Scrape down the sides and bottom of the bowl, then divide the mixture evenly between the prepared pans. Use an offset spatula to smooth the top of the batter. Bake the cakes for 35-40 minutes, rotating the pans halfway through the baking time, until a toothpick inserted in the center comes out clean. Transfer the pans to a wire rack to cool for about 30 minutes, then turn the cakes out onto the rack to cool completely.

To make the coffee buttercream, whisk the flour and sugar together in a medium saucepan. Add the milk and cream and whisk to combine. Cook over medium heat, whisking occasionally, until the mixture comes to a boil and has thickened, about 10-15 minutes. Transfer the mixture to the bowl of a stand mixer fitted with the paddle attachment and beat on high speed until the mixer bowl cools to room temperature, 7-9 minutes.

Reduce speed to low and add the butter, a few pieces at a time, and mix until thoroughly incorporated. Increase speed to medium high and beat until the frosting is light and fluffy, an additional 1-2 minutes. Add the vanilla and coffee extracts and continue mixing until combined. At this point, if your frosting is too loose, it can be refrigerated. On the other hand, if it’s too firm, you can heat it over a pot of simmering water until it reaches your desired consistency.

Assemble the cake by placing one layer on a cake stand. Level as needed, then top with a heaping cup of buttercream. Spread the buttercream nearly to the edges. Repeat with the next layer. Once all three layers are stacked, spread a thin layer of frosting over the top and sides to create a crumb coat. Refrigerate for 15 minutes. Spread the remaining frosting over the top and sides of the cake and refrigerate for another 15 minutes while making the ganache.

To make the chocolate ganache, place the chocolate, butter and corn syrup in a bowl (preferably one with a pour spout) set over a pot of simmering water. Using a rubber spatula, stir the mixture until smooth and combined. Very slowly pour about ¾ cup of glaze over the frosted cake. Use a small offset spatula to carefully smooth it out to the edges. Refrigerate for about 5 minutes to set. Remove the cake from the refrigerator and slowly pour over the remaining ganache, letting it drip down the sides in thick streams. Chill the entire cake for about 20 minutes to set. Serve at room temperature.

The cake can be stored, covered in a cake container, at room temperature for up to 3 days.