Preheat the oven to 350 degrees F. Grease an 8×8 inch pan with butter and set aside. In a measuring cup, whisk the hot coffee and butter until the butter melts, then set it aside until ready to use.
In a large bowl, whisk together the eggs, buttermilk and vanilla extract. Stir in the sugar, flour, cocoa, baking powder, soda and salt. Once it’s about halfway mixed, pour in the coffee/butter mixture and stir until you have a smooth batter. Stir in the chopped chocolate. Pour the batter into the greased pan and bake for 40 to 45 minutes, or until the cake is just set in the middle. Let cool completely.
Once cool, poke the top of the cake with a fork – lots of holes for the delicious chocolate milk to stream into. Whisk together the condensed milk, evaporated milk and chocolate milk. Pour it over top (you can do it in batches) evenly and watch it sink into the cake. Refrigerate the cake for 30 to 60 minutes before serving. To serve, top with whipped cream (I like to use unsweetened whipped cream or coconut whipped cream since the cake is rich) and chocolate shavings. Keep the cake in the fridge!