In a large bowl, beat butter for 1 minute on medium speed until smooth and creamy. Add sugar and brown sugar and beat until fluffy. Beat in egg, vanilla, and peppermint extract on high speed. Scrape down the sides and bottom of the bowl as needed. In a separate bowl, whisk flour, cocoa powder, baking soda, espresso powder, and salt together. On low speed, slowly mix into wet ingredients until combined. The dough will be quite thick. Mix in chocolate chips. The cookie dough will be sticky. Cover dough tightly with plastic wrap and chill for at least 3 hours or overnight. Chilling is necessary for this cookie dough. Remove cookie dough from refrigerator and allow to sit at room temperature for 20 minutes. Preheat oven to 350 degrees. Line two large baking sheets with parchment. Set aside. Scoop and roll balls of dough, about 1 1/2 Tbsp. of dough each. Place on baking sheets. Bake for 8-9 minutes. Allow to cool for 5 minutes. Transfer to cooling rack to cool completely. Melt white chocolate in microwave. Melt in 15 second increments, stirring after each increment until completely melted and smooth. Dip each cookie halfway into white chocolate and place onto a parchment lined baking sheet. Sprinkle with crushed candy canes on top or chocolate. Repeat with remaining cookies. Place in refrigerator to allow chocolate to set.