Preheat the oven to 350 degrees F and grease two 6-inch round cake pans.
In a large bowl, whisk together the flour, 1/2 cup black cocoa powder, granulated sugar, baking powder, baking soda, and salt.
In a second bowl, beat the eggs, 1/2 cup milk, oil, and vanilla until smooth.
Pour the wet mixture into the dry ingredients and stir until just combined.
Divide the batter evenly between the two pans and bake for 22 to 25 minutes, until a toothpick comes out clean.
Cool the layers in the pans for 10 minutes, then remove and cool completely on a wire rack.
Beat the softened butter until creamy, then add the powdered sugar and remaining 2 tbsp black cocoa powder.
Mix in the remaining 2 tbsp milk until the frosting reaches a spreadable consistency.
Place one cooled layer on a plate, spread with half the frosting, add the second layer, and frost the top and sides.
Drizzle or pipe the melted dark chocolate into small bat shapes on parchment paper, let them set, then place them on the frosted cake.