In a medium saucepan, combine semi-sweet chocolate, dark chocolate, and vanilla extract. In a separate small pot, heat heavy cream and sugar over medium heat, stirring until the sugar dissolves. Pour the warm cream mixture over the chocolate, whisking until smooth and glossy. Chill the frosting in the refrigerator for at least 30 minutes until it thickens and reaches a spreadable consistency.

Preheat your oven to 350°F (175°C) and grease two 9-inch round cake pans. In a large bowl, whisk together all-purpose flour, granulated sugar, dark brown sugar, cocoa powder, baking powder, baking soda, and salt. In a separate bowl, combine vegetable oil, eggs, instant coffee granules mixed with hot water, and vanilla extract. Gradually add the wet mixture to the dry, mixing until smooth.

Divide the batter evenly between the prepared pans, smoothing the tops with a spatula. Bake in the preheated oven for 30–35 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs. Remove the cakes from the oven and allow them to cool in the pans for 10 minutes before transferring to wire racks to cool completely.

While the cakes cool, prepare the coffee soak by brewing a concentrated cup of coffee. In a small bowl, whisk together the warm brewed coffee and a bit of sugar until dissolved. Allow this mixture to cool to room temperature.

Once the cakes are completely cool, slice each cake horizontally to create four equal layers. Place the first layer on a serving platter and generously brush it with the cooled coffee soak.

Spread a layer of the chilled espresso frosting over the soaked cake layer, then repeat this process with the remaining layers, stacking them carefully to create an impressive height.

After layering, apply a thin coat of frosting around the entire cake to seal in crumbs, known as the crumb coat. Smooth it gently with a spatula, then place the cake in the refrigerator for about 20 minutes to set.

Once chilled and set, remove the cake from the refrigerator. Spread the remaining espresso frosting generously over the top and sides of the cake, smoothing it out for a clean finish. Decorate with chocolate shavings or espresso beans.