Heat oven to 350°F; line baking sheets with parchment.
Whisk flour, cocoa, baking soda, and salt in a medium bowl; set aside.
Beat butter and both sugars in a large bowl about 3 minutes until light and fluffy. Mix in egg, vanilla, and peppermint extract.
Gradually mix flour mixture into butter on low just until combined. Fold in chips and ¼ cup candy canes.
Put remaining ¼ cup candy canes in a shallow bowl. Scoop rounded tablespoons of dough; roll into balls and coat in peppermint.
Space cookies 2 inches apart. Bake 9-11 minutes until edges set and centers look slightly soft. Cool on sheet 5 minutes; transfer to rack to cool completely.