In a medium bowl, whisk together flour, cocoa powder, baking powder, baking soda, and salt.
In a large bowl, combine melted butter, granulated sugar, and brown sugar and whisk smooth. Add eggs and peppermint extract and whisk until smooth and combined.
Stir in dry ingredients until just combined, then fold in ½ cup crushed peppermint candies. Cover with plastic wrap and chill for 2 hours.
Preheat oven to 350°F. Line three baking sheets with parchment paper.
Scoop dough into 1 Tablespoon portions and roll into balls. Chill in freezer for 10 minutes.
Fill two bowls each with granulated sugar and powdered sugar, for rolling. Transfer remaining ¼ cup crushed peppermint candies into a resealable plastic bag. Use a rolling pin to crush them into a fine powder. Mix peppermint candy powder into the powdered sugar bowl.
Roll cold cookie dough balls in granulated sugar and then powdered sugar and place on prepared baking sheets. Roll balls once more in powdered sugar to get a thick coating, then arrange 3-inches apart on the baking sheets.
Bake until cookies are puffed and cracked and edges are just set, 10-12 minutes. Let cool completely on a baking sheet.
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