Preheat the oven to 350ºF. Put the softened butter and both types of sugars in a large bowl. Use a hand mixer to blend together until smooth.
Add the egg, vanilla extract, and peppermint extract to the bowl, then mix on high speed until the mixture becomes fluffy.
In a separate medium bowl, whisk together the flour, cocoa powder, baking powder, and salt.
Add the wet mixture to the dry mixture. Use the hand mixer to blend together. As you mix, slowly drizzle in the milk until everything is incorporated.
Stir in the chocolate chips. Cover the bowl with plastic wrap and refrigerate for 30 minutes.
Line a baking sheet with parchment paper. Use a cookie scoop to measure out the cookie dough onto the sheet, and leave space between each scoop of dough to allow for expansion during baking. Bake for 10–15 minutes.
Remove from the oven and let cool. In the meantime, melt the white chocolate. Once the cookies have cooled for about 10 minutes, drizzle some of the melted white chocolate over the cookies. For a nice design, alternate between dipping them in the chocolate and drizzling the chocolate over them. Stick the crushed candy bits into the wet chocolate.