Using a stand mixer or hand-held mixer, beat the butter on medium speed until smooth and creamy.
Add both sugars and beat on medium speed until lighter in color.
Beat in the egg, vanilla, and peppermint extracts on high speed until combined. Scrape down the sides of the bowl as necessary.
In a separate bowl, combine the flour, cocoa powder, baking soda, espresso powder, and salt.
On a slow speed, slowly add the dry ingredients into the wet ingredients until combined. The cookie dough will be very thick.
Switch the mixer to high speed and add in the chocolate chips until combined.
Cover the dough with aluminum foil or plastic wrap tightly and place in the refrigerator for a minimum of 3 hours and maximum of 3 days. It's best to chill them overnight.
Remove the dough from the fridge and let it sit at room temperature for 20-30 minutes so that it's easier to scoop.
Preheat the oven to 350 F degrees.
Line two baking sheets with parchment paper.
Scoop dough using a melon baller and roll into a ball shape. Place each ball on the baking sheet.
Bake for 8-10 minutes. Even when the cookies are finished, the centers will be very soft. Let the cookies cool for 5 minutes on the cookie sheet before transferring them to a cooling rack to cool completely.
Melt the white chocolate chips in the microwave or over a double boiler. Place the chocolate chips in a microwave safe bowl, heat them in the microwave in 15 second increments, stirring between each increment until the chips are completely melted.
Dip each cookie halfway into the white chocolate and place them onto parchment paper. Sprinkle the melted chocolate with crushed peppermint candies.
Place the cookies in the fridge to set.