In a mixing bowl, combine dark chocolate and instant coffee. In a saucepan, heat heavy cream until just beginning to simmer. Pour hot cream over chocolate and whisk until smooth. Chill in refrigerator until set, about 30 minutes.

Preheat your oven to 350°F (175°C). In a large bowl, whisk together flour, cocoa powder, baking powder, baking soda, dark brown sugar, granulated sugar, and salt until no lumps remain.

In another bowl, combine eggs, vegetable oil, vanilla extract, milk, and hot brewed coffee and whisk until fully integrated.

Gradually pour wet mixture into dry ingredients, stirring gently until just combined.

Grease and flour two 9-inch round cake pans. Divide batter evenly and smooth tops. Bake for 30-35 minutes until a toothpick comes out clean.

Remove from oven and cool on a wire rack for about 10 minutes. Gently run a knife around the edges and invert cakes onto the rack to cool completely.

Mix brewed coffee with sugar to create a coffee soak. Brush generously on the tops of each layer.

Level the tops of the cooled layers with a serrated knife if necessary. Layer with care if desired.

Assemble the cake by layering and spreading frosting between each layer. Apply a thin crumb coat around the cake.

Chill for 20-30 minutes to set the crumb coat, then frost the top and sides to finish.