In a medium bowl, combine finely chopped dark chocolate, cocoa powder, and a pinch of salt. In a small saucepan, heat heavy cream and sugar over medium heat, stirring until the sugar dissolves. Pour the hot cream mixture over the chocolate and whisk until smooth and glossy. Chill the frosting in the refrigerator for about 30 minutes, or until it reaches a spreadable consistency.

Preheat your oven to 350°F (175°C) and grease two 9-inch round cake pans. In a large mixing bowl, whisk together the dry ingredients: all-purpose flour, cocoa powder, dark brown sugar, and instant coffee. In a separate bowl, mix the wet ingredients: melted butter, eggs, and hot brewed coffee. Gradually combine the wet and dry mixtures until smooth and well-blended.

Evenly pour the cake batter into the prepared pans and bake in the preheated oven for 25–30 minutes, or until a toothpick comes out clean. Let them cool in the pans for 10 minutes before transferring them to wire racks to cool completely.

Whisk together ½ cup of brewed coffee and 1 tablespoon of cocoa powder until dissolved. Allow this mixture to cool for a few minutes.

Once cooled, level the tops of the cake layers and slice each in half. Brush a generous amount of coffee soak on each layer and spread frosting between layers.

Apply a thin crumb coat of frosting over the entire cake and chill for 20 minutes. Apply the final layer of frosting, smoothing it out for a clean finish.