Chop the chocolate into rough chunks. Chop the butter into rough chunks.Add both to a small sauce pan with a stick-free surface, and over medium to low heat, slowly stir until both are melted. Be careful not to let it burn. You can also melt both over a water bath.
Put the sugar and arrowroot in a large mixing bowl.Pour in melted butter/chocolate mixture, and the vanilla. And add about 2 tbsp of milk. Blend until creamy, adding more milk to reach a frosting texture.
Cover frosting bowl with a soaking-wet paper towel while you work with frosting. I advise you frost as fast as possible while the frosting is shiny; it hardens faster with the arrowroot.
If you want to put a creamy center in a few of your cupcakes, dig out the center core of each cupcake with the other side of the piping tip - it pops the core right out! Then pump icing inside so the cupcakes have a filling.
I piped the icing rosettes on top with a piping bag and French tip, 4B. I hope you love my reduced sugar icing!