In a large bowl or stand mixer, beat together butter and sugars until light and fluffy. Mix in egg, vanilla and peppermint extract. Scrape bowl as needed. Add salt, baking soda and cocoa powder. Mix until just combined. Add flour, mixing until streak free and fully combined. Stir in chocolate chips and white chocolate peppermint chunks by hand. Transfer to a clean bowl or storage container. Chill until firm but manageable, at least several hours or overnight. 

Preheat oven to 350°F. Line a baking sheet with a silicone baking mat or parchment paper. 

Using a medium cookie scoop, scoop and shape dough into smooth balls. Optionally, add extra chocolate chips and white chocolate peppermint chunks to the tops of each ball of dough. 

Bake for 10 minutes. Allow cookies to sit on the tray for 2 minutes prior to transferring to a wire rack to cool completely. Store cooled cookies in an airtight container.