Melt 100 grams of high quality dark chocolate in a heat-proof bowl placed over a pot of gently simmering water on the stove. Use a spatula to stir around the chocolate pieces over the heat until everything is smooth and melted.
Set the chocolate aside to cool to almost room temperature.
While the chocolate is cooling, add the room temperature butter to the bowl of a stand mixer fitted with a whisk attachment.
Whip the butter on medium-high speed until it's smooth (about 1 minute).
Add the powdered sugar and the cocoa powder. Start the mixer again and slowly increase the speed as the mixture begins to come together. Scrape down the sides and the bottom of the bowl as needed.
Once the frosting begins to thicken, add the melted chocolate, but only if it has cooled to almost room temperature.
Beat in the chocolate and scrape down the sides of the bowl to make sure all the powdered sugar and cocoa powder are completely incorporated.
This will leave you with a very thick frosting, so add the milk and continue whipping on high speed for about 45 seconds - 1 minute. If you're not satisfied with the texture (it's too stiff) add a bit more milk 1/4 tsp at a time until you achieve the consistency you're looking for.
Once the cupcakes have cooled completely spread frosting onto each one, or pipe the frosting in a circular motion using a piping bag and a 1-inch round tip.
If desired, use a microplane zester to shave some dark chocolate onto the top of each cupcake.