Preheat oven to 350°F. Line 2 baking sheets with parchment paper and set aside.
With a hand or stand mixer, cream together the softened butter, light brown sugar, and granulated sugar for about a minute until light and fluffy. Add in the eggs, vanilla extract, and peppermint extract and mix until combined.
Add in the flour, cocoa powder, baking soda, and salt and mix until just combined. Fold in the chocolate chips.
Use a medium cookie scoop to scoop out the dough, rolling each into a ball. Place the dough a few inches apart on the prepared baking sheets. Top the balls of dough with more chocolate chips, if desired.
Bake cookies for 11-12 minutes. They will still look a bit soft in the center, but that's perfect. Allow them to cool for 4-5 minutes, then transfer them to a cooling rack.
Once the cookies are cool, start the chocolate drizzle. Melt the chopped semisweet chocolate. Pour it into a piping bag or small plastic storage baggy. Snip the corner off the bag and drizzle the melted chocolate over half of the cookie. Then, sprinkle the crushed candy cane bits over the chocolate drizzle. Allow the chocolate to set. Enjoy!