Prep the pans: Preheat oven to 325°F (163ºC). Prepare two 9-inch pans with nonstick baking spray and 9-inch parchment circles.
Whisk the dry ingredients: In a large bowl, whisk together all the dry ingredients really well. This step matters more than it seems because it ensures an even texture and no cocoa clumps.
Mix the wet ingredients: In a separate bowl, whisk together the eggs (2), egg yolk (1), oil (1/2 cup), sour cream (3/4 cup), buttermilk (1/2 cup), and vanilla (2 teaspoons) until smooth and creamy.
Combine the batter: Pour the wet ingredients into the dry ingredients and mix just until combined. The batter will be thick and rich at this stage.
Add the hot coffee: Slowly stream in the hot coffee (3/4 cup) while mixing. You’ll see the batter loosen into a smooth, glossy, pourable consistency. That thin batter is exactly what creates a soft, tender crumb.
Bake the cakes: Divide the batter into two greased 9-inch round pans, about 665g per pan, or one 9x13-inch pan. Tap the pans gently to release air bubbles. Bake at 325°F (163ºC) for 25–29 minutes, or 32–38 minutes for a 9x13-inch pan, until the centers lose their shine and spring back slightly when lightly touched. A toothpick should come out with a few moist crumbs, not wet batter. Cool the layers: Cool the cakes in the pans for 10–15 minutes, then turn them out and cool completely before frosting.
Melt the chocolate mixture: While the cake is baking, make the frosting by adding the chocolate chips (12 ounces), espresso powder (1 teaspoon), if using, corn syrup (1/4 cup), and 5 tablespoons of water to a microwave-safe bowl. Microwave for 1 minute and stir until smooth and melted. Set aside to cool.
Beat the butter: In a separate mixing bowl, beat the butter (2 cups) until smooth and lighter in color.
Build the frosting: Add the measured, then sifted, cocoa powder (1 1/4 cup) and powdered sugar (2 1/4 cups), then add the salt (pinch) and vanilla (2 teaspoons). Beat on low speed until incorporated, then add the cooled melted chocolate mixture.
Whip the frosting: Continue beating on low speed, then high speed, until fluffy and smooth. If the frosting is too stiff, add up to 2 tablespoons of water. If the frosting is too soft, cool it in the refrigerator for a few minutes, then beat on high speed until smooth. The frosting will be the consistency of soft, spreadable fudge.
Fill the cake: To assemble, place the bottom cake layer, bottom side down, on a cake plate. Add ½ to 1 cup frosting to the top and spread it evenly with an offset spatula.
Stack the layers: Add the top cake layer, bottom side up. Add 1 cup frosting to the top, then spread it to the sides, adding more as needed.
Frost and finish: Add more frosting to the top of the cake and spread it until it is even and fairly smooth on the top and sides. Using the offset spatula, drag the tip through the frosting while spinning the cake on a turntable to create a line running from the bottom to the top on the sides, then from the outside to the inside on the top of the cake. Decorate with chocolate swirls, if desired.