For the cake, preheat the oven to 350 degrees Fahrenheit and grease a 9"X13" cake pan.
In the bowl of an electric mixer, add chocolate cake mix, sour cream, eggs, melted butter, vanilla extract, and buttermilk. Mix until incorporated, scraping down the sides with a spatula in between.
Pour and spread evenly into prepared pan.
Bake for approximately 25 to 30 minutes, or just until a toothpick inserted into the center comes out clean. Check it often so you don't over bake it.
Allow the cake to cool completely on a cooling rack. Then use the round end of a wooden spoon to poke holes all over the in cake.
Stir together the melted chocolate chips and sweetened condensed milk until combined. You'll need to work quickly because the chocolate will cause the mixture to set and will become difficult to pour if you take too long. Pour the mixture into the holes. Allow that to set completely.
Prepare the frosting by creaming together (in the bowl of an electric mixer) the butter, powdered sugar, baking cocoa, vanilla extract and just enough milk for thinning. Mix until nice and creamy and spreadable. Spread over cooled cake, sprinkle with chocolate shavings or mini chocolate chips, and serve. Let it chill in the fridge if you prefer cool cake.