Stir together brownie mix, cocoa, and crushed peppermint candies in a large bowl. Add contents of syrup pouch, water, egg, and oil, beating until well blended. Refrigerate until firm enough to roll, about 1 hour.

Heat the oven to 350 degrees F (175 degrees C). Line a cookie sheet with parchment paper or lightly grease. Remove wrappers from candies.

Shape dough into 1-inch balls. Roll balls in powdered sugar and place on prepared cookie sheet.

Bake in the preheated oven until set, 9 to 11 minutes. Cool for 2 minutes. Press candy piece into the center of each cookie. Slide parchment paper and cookies to a wire rack or remove cookies from cookie sheet to a wire rack. Cool completely.