Preheat oven to 350 ºF. In a food processor finely grind peppermint candies and 1/3-cup sugar to a powdery consistency; transfer to a small bowl. In a large bowl, cream butter, shortening, and remaining 1 cup sugar until fluffy. Add eggs and extracts; beat until smooth. In a medium bowl, combine flour and salt.
Add dry ingredients to creamed mixture; stir until a soft dough forms. Shape dough into 1-inch balls. Roll balls in candy mixture. For best results, place 6 cookies at a time on an ungreased baking sheet.
Bake 8 minutes; immediately roll hot cookies in candy mixture. Transfer to a wire rack to cool completely. Repeat with remaining dough. Store in an airtight container.