Preheat oven to 350 degrees F.
Line 24 muffin tins with cupcake liners and set aside.
In a large bowl, whisk together sugar, flour, cocoa, baking powder, baking soda and salt.
Add remaining ingredients, except boiling water and chocolates and beat on medium speed for 2 minutes.
Stir in boiling water until mixed then pour into cupcake liners, filling about 2/3 full (this batter is thin, so don't be alarmed).
Sprinkle peppermint baking chips, evenly, onto the batter in each liner and swirl with a toothpick to mix in.
Bake for 23-25 minutes, until a toothpick comes out clean (the center where the chocolate is will look a little wet, this is ok)
Cool completely on wire racks before frosting
To make frosting:
Whip softened butter in the bowl of an electric mixer until light and fluffy
Add vanilla, peppermint extract and 1/3 of the powdered sugar
Blend until creamy, then add half of the milk and cream and another third of the powdered sugar, scraping down the bowl occasionally
Add the remaining milk and cream and sugar and blend until smooth, creamy and spreadable
Frost cupcakes using your favorite decorating tip and sprinkle with crushed peppermint