Preheat the oven to 350 degrees and line two large baking sheets with parchment paper.
1. Cream the butter and brown sugar until light and fluffy, about 2-3 minutes. Scrape down the sides of the bowl, then add the egg, peppermint extract, and vanilla extract. Mix for about 30-60 seconds.
2. In a separate bowl, whisk together the flour, cocoa powder, espresso powder, baking soda, and salt.
3. Add the dry ingredients to the wet, mixing until just incorporated. Fold in the semi-sweet chocolate chips, white chocolate chips, and crushed peppermints.
4. Use a 1-oz scoop to portion out the dough then place the mounds of dough on the lined baking sheet at least 2-inches apart.
5. Bake the cookies in the preheated 350-degree oven for 11-14 minutes until the edges are just set.
6. Allow the baked cookies to cool on the baking sheet for 10 minutes before transferring to a rack to cool completely.
To top the cookies with chocolate if desired: Once the cookies are cool, drizzle with melted chocolate and sprinkle additional crushed mints on top of the cookies. This will cause the candies to bind to the cookie when the chocolate cools.
Melt the chocolate chips in short 20-30 second bursts in the microwave, stirring well between heating. Once melted, dollop a spoonful of melted chocolate on each cookie and sprinkle with peppermint candy. The chocolate will solidify as it cools.