In the bowl of a stand mixer fitted with a paddle attachment or in a large bowl with an electric hand mixer, cream together the unsalted butter, light brown sugar, and granulated sugar until smooth and creamy. Add in the eggs, vanilla extract, and peppermint extract and mix until smooth.
Add in the all-purpose flour, dark cocoa powder, baking soda, and salt and mix on low speed until the cookie dough forms.
Portion the cookie dough using a large cookie scoop (3 tablespoon). Chill the cookie dough balls for 30 minutes.
Preheat the oven to 350℉ (177℃). Prepare baking sheet pans with silicone baking mats or parchment paper sheets.
Bake the cookies for 11 to 12 minutes until the edges are set. Allow the cookies to cool on the pan for 2 minutes and then transfer to a wire rack to cool completely.
In a microwave-safe bowl, heat the white melting chocolate or almond bark in the microwave in 15 seconds intervals, mixing in between each interval, until the chocolate is melted and smooth. Dip half the cookies in the melted white chocolate and place on a parchment lined baking sheet. Add a sprinkling of crushed candy canes or peppermint candies before the white chocolate sets.