Preheat oven to 350°. Cut sugar cookie dough into 8 pieces. Combine the dough pieces, 1/4 cup crushed hard peppermint candies, and 1/2 cup powdered sugar in a bowl or electric mixer. Let the mixture chill in the refrigerator for 30 minutes. Coat hands in flour, and roll chilled dough into 1/2-inch diameter balls. Place the balls 2 inches apart on parchment paper–lined baking sheets. Bake for 9-10 minutes or until set. Cool cookies slightly on cooling rack. While cookies are still warm, sprinkle the tops with 1/4 cup powdered sugar and 2 tablespoons crushed hard peppermint candies.