Preheat oven to 350°F. Microwave chocolate and butter in large microwavable bowl on HIGH 1 to 2 minutes or until butter is melted. Let stand 10 minutes to cool slightly. Add 1/2 cup of the sugar, egg and peppermint extract. Beat with electric mixer on medium speed until well blended. Gradually beat in flour on low speed until well mixed.
Shape dough into 1-inch balls. Press a chocolate candy into the center of each ball, forming dough around the candy to completely enclose it. Roll in remaining 1/2 cup sugar to coat. Place 1 inch apart on greased baking sheets.
Bake 9 to 11 minutes or until cookies are set. Cool on baking sheets 5 minutes. Remove to wire racks; cool completely.