Prepare the Cake Pans: Instruction. Preheat the oven to 350°F. Spray two 9-inch round baking pans with non-stick baking spray, line the bottoms with parchment rounds, and spray the parchment as well. Set the prepared pans aside.
Combine the Dry Ingredients: Instruction. Sift the flour, cocoa powder, baking soda, baking powder, and salt together into a large bowl. Set the mixture aside.
Beat the Butter: Instruction. Using a stand mixer fitted with the paddle attachment, or a large bowl and handheld electric mixer, beat the room-temperature butter on medium speed for about 1 minute, until smooth.
Add the Sugars: Instruction. Gradually add the granulated sugar and light brown sugar, adding them one at a time and beating until incorporated into the butter. Increase the mixer to high speed and beat for about 4 minutes, until the mixture is light and fluffy, scraping down the sides and bottom of the bowl as needed. Incorporate the Eggs: Instruction. Add the eggs and egg yolk one at a time, beating well after each addition and scraping down the bowl as necessary. Add the vanilla extract and beat until combined.
Mix the Wet Ingredients: Instruction. In a spouted measuring cup, combine the vegetable oil and room-temperature sour cream.
Alternate the Dry and Sour Cream Mixtures: Instruction. Set the mixer to its lowest speed. Add the dry ingredients in three additions, alternating with the sour cream mixture in two additions. Mix only until the ingredients are just combined; a very light trail of dry ingredients should still be visible when you stop the mixer. Add the Coffee: Instruction. Pour the hot, freshly brewed coffee into the batter and allow it to sit undisturbed for 30 seconds. Then gently stir with a rubber spatula until the batter is evenly combined.
Fill the Pans: Instruction. Divide the batter evenly between the prepared pans, approximately 850 grams of batter per pan, and smooth the surfaces with a rubber spatula.
Bake the Cake: Instruction. Bake at 350°F for 38–45 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs attached.
Cool the Layers: Instruction. Place the cakes in their pans on a wire rack and cool for 20 minutes. Invert the cakes onto the rack and allow them to cool completely, about 1 hour.
Chop the Chocolate: Instruction. Finely chop the semi-sweet chocolate with a large chef’s knife, then place it in the bowl of a stand mixer fitted with the whisk attachment.
Heat the Cream Mixture: Instruction. Place the heavy cream and light corn syrup in a small saucepan and heat over medium-high heat until the mixture comes just short of a rolling boil. Remove from the heat.
Make the Chocolate Base: Instruction. Pour the hot cream mixture over the chopped chocolate and leave it undisturbed for 2 minutes. Gently stir with a rubber spatula or metal spoon until the chocolate has completely melted and the mixture is smooth and glossy. Stir in the vanilla extract. Add the Butter: Instruction. With the mixer running at medium speed, add the room-temperature butter 1 tablespoon at a time, beating well after each addition and waiting until each portion is fully incorporated before adding more. Beat in the fine sea salt.
Chill the Frosting: Instruction. Loosely cover the frosting and refrigerate for about 1 hour, or until it becomes firm enough to spread. The frosting can be prepared up to 24 hours ahead and refrigerated covered; bring it to room temperature before using.
Trim the Cake Layers: Instruction. Using a long serrated knife, carefully remove the domed tops from both cooled cake layers so they are smooth and even. Set the trimmed cake scraps aside for decorating.
Split the Layers: Instruction. Slice each cake layer horizontally in half, creating four even cake layers in total.
Begin Assembly: Instruction. Place one cake layer on a large plate or cake stand and spread ½ cup of chocolate frosting evenly over the top.
Stack the Cake: Instruction. Place another cake layer on top of the frosting and repeat the layering process until all four cake layers are stacked, finishing with the final cake layer on top.
Frost the Cake: Instruction. Spread all of the remaining frosting over the top and sides of the assembled cake, covering it completely.
Prepare the Cake Crumbs: Instruction. Use your hands to crumble the reserved cake scraps into fine crumbs.
Decorate with Crumbs: Instruction. Gently pat the cake crumbs around the sides of the frosted cake. Any excess crumbs may be discarded or enjoyed as a snack.
Set the Cake: Instruction. Allow the finished cake to stand for 20 minutes before slicing.
Serve or Store: Instruction. Serve the cake after it has set, or refrigerate it for up to 5 days. Bring the cake back to room temperature before serving.
