To begin the filling base, whisk together granulated sugar, all-purpose flour, and salt in a medium saucepan. Gradually incorporate the milk, whisking continuously to avoid lumps, then heat over medium while stirring until it thickens to a pudding consistency. Transfer to a heatproof bowl, press wax paper directly on the surface, and let it cool completely to room temperature.

For the cake, preheat the oven to 350°F (175°C). Line and grease two 8-inch round cake pans. In a large bowl, combine flour, brown sugar, granulated sugar, cocoa powder, baking soda, and salt. Mix in melted butter and oil thoroughly. Incorporate the eggs, egg yolk, and vanilla until smooth. Add buttermilk gradually, stirring well, followed by the hot coffee. Divide the batter evenly between pans and bake for 33–35 minutes. Let the cakes cool in the pans for 15 minutes, then transfer to wire racks to cool completely.

To prepare the filling, beat softened butter on high speed until fluffy. Lower the mixer to medium and gradually incorporate the cooled filling base by the spoonful. Once blended, add vanilla extract and whip on medium-high until the mixture is smooth and aerated. Chill in the refrigerator for 10–20 minutes to firm slightly.

For the ganache, place chocolate and heavy cream in a microwave-safe bowl. Heat on high for 35 seconds, stir, then microwave for an additional 25 seconds. Stir until fully smooth, reheating in 25-second intervals if necessary. Let cool until it reaches a spreadable consistency.

Assemble by leveling the cakes if needed. Position one layer on a serving plate and spread the filling evenly over it. Add the second layer on top, smoothing the sides. Freeze the cake for 10–15 minutes before applying the ganache. If the ganache hardens too much, briefly microwave until just spreadable. Coat the cake evenly with ganache. Chill for at least 15 minutes to set before slicing and serving.