Preheat oven to 325 degrees F. Butter three 8 inch round cake pans, line them with parchment paper, and butter the parchment, Dust the parchment with flour and knock out excess flour.
In medium bowl, mix the cocoa powder and sour cream with 1 1/4 cups hot water and set aside to cool.
In a large bowl, sift the flour, baking soda, baking powder, and salt together and set aside.
Using a standing mixer fitted with a paddle attachment, beat the butter and shortening together on medium speed until light and fluffy, about 5 minutes – the mixture will appear to string or ribbon throughout the bowl. Add the sugars and beat on medium speed until light and fluffy, about 5 more minutes. Add the eggs, one at a time, mixing about 10 to 15 seconds after each addittion until the egg is incorporated into the mixture. Then turn the mixer to low, add the vanilla, and beat until incorporated. Scrape down the sides of the bowl and mix again for 30 seconds.
Beginning with the dry ingredients, add the dry mixture and the cocoa mixture to the mixer bowl in three alternating parts, ending with the dry. Divide the batter amond the prepared pans. Use an offset spatula to level the batter. Bake the cakes for 35-40 minutes, rorating the pans halfway through the baking time, until a toothpick inserted in the center comes out clean. Transfer the pans to a wire rack and cool for 30 to 45 minutes. Turn the cakes out onto the rack and let them cool completely. Remove the parchment.
Make the coffee buttercream: In a medium, heavy bottomed saucepan, whisk the sugar and flour together. Add the milk and cream and cook over medium heat, whisking occasionally, until the mixture comes to a boil and has thickened, about 10 to 15 minutes.
Transfer the mixture to the bowl of a standing mixer fitted with the paddle attachment. Beat on high speed until cool (this takes about 7-9 minutes; however, you can speed up the process by pressing bags of frozen berries or frozen corn around the sides and bottom of the mixing bowl). Reduce the speed to low and add the butter; mix until thoroughly incorporated. Increase the speed to medium high and beat until the frosting is light and fluffy, about another 1-2 minutes.
Add the vanilla and coffee extracts and continue mixing until combined. If the frosting is too soft, put the bowl in the refrigerator to chill slightly, then beat again until it is the proper consistency. If the frosting is too firm, set the bowl over a pot of simmering water and beat with a wooden spoon until it is the proper consistency.
To assemble the cake: Place one cake layer on a serving platter. Trim the top to create a flat surface, and evenly spread about 1 1/4 cups frosting on top. Add the next layer, trim and frost it, then add the third layer. Spread a very thin layer of frosting over the sides and top of the cake and put it in the refrigerator for about 15 minutes to firm up. (This is known as the crumb coating and will help you keep loose cake crumbs under control when you frost the outside of the cake.) Spread the sides and top of the cake with the remaining frosting. Refrigerate it for 15 minutes to firm it up.
Make the chocolate glaze: Place the butter, chocolate, and corn syrup in the top of a double boiler. Using a rubber spatula, stir the mixture until the chocolate and butter are completely melted and smooth.
Remove the pan from the heat and stir the glaze to release excess heat. Drizzle glaze over the cake. Refrigerate the cake about 15 minutes to set the glaze before serving.
Glaze the cake: Line a rimmed baking sheet with parchment paper. Place your cake on a wire rack over the baking sheet. Slowly pour about 3/4 of a cup of the glaze over the cake. Use a small offset spatula to smooth it out to the edges. Place the cake in the refrigerator for 5 minutes to set the glaze. Remove from the refrigerator and slowly pour the rest of the glaze over the cake. It should run down the sides in thick streams. You should be able to control the size and length of the streams by the pour. Feel free to experiment, and have no fear n plaing around. This is the fun part, and there is no right or wrong way. Garnish with chocolate covered espresso beans. Chill the entire cake for approximately 20 minutes, or until glaze is set, then transfer to a cake plate. Serve at room temperature.