In a bowl, cream butter and sugars together for a few minutes. Add egg then stir in the peppermint extract. Add flour, Dutch process cocoa powder, baking soda, and salt. Mix until just well combined.
Using a medium cookie scoop, form cookie doughs into balls (~1 1/2 tablespoons size). Place the cookie dough balls on a baking sheet and freeze the dough balls for at least 20 minutes.
Preheat oven to 350ºF. Line a baking sheet with parchment paper and place dough balls on the baking sheet. Bake for about 10-11 minutes. Remove from oven and let them cool completely.
While you’re waiting for the cookies to cool, make the chocolate frosting. In a bowl, add powdered sugar, cocoa powder, and butter. Mix until well combined. Add whipping cream and vanilla extract. Mix until smooth.
Spread chocolate frosting on top of the cooled cookies then garnish with crushed peppermint candies. Enjoy!