Preheat oven to 350°F and line baking sheets with parchment paper.
In a medium bowl, whisk together flour, cocoa powder, baking soda, and salt. Set aside.
In a large bowl, beat butter, granulated sugar, and brown sugar until light and fluffy, about 3 minutes. Add egg, vanilla extract, and peppermint extract, mixing until well combined.
Gradually add the flour mixture to the butter mixture, mixing on low speed until just combined. Fold in chocolate chips and ¼ cup of crushed candy canes.
Place remaining ¼ cup crushed candy canes in a shallow bowl. Scoop dough by rounded tablespoons, roll into balls, and roll each ball in the crushed peppermint.
Place cookies on prepared baking sheets, spacing 2 inches apart. Bake for 9-11 minutes until edges are set but centers still look slightly soft. Cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.