In large bowl, beat butter and powdered sugar with electric mixer on medium speed until fluffy. On low speed, beat in flour and peppermint extract.
On ungreased cookie sheet, pat dough into 6-inch square, about 3/4 inch thick. Cover; refrigerate 30 minutes.
Heat oven to 325°F. On cookie sheet, cut dough into 8 rows by 8 rows, making 64 squares. With knife, separate rows by 1/4 inch.
Bake 28 to 35 minutes or until set and edges are just starting to turn golden. Meanwhile, in small bowl, mix crushed candy and granulated sugar. In small resealable food-storage plastic bag, place melted candy coating. Seal bag; cut tiny hole in corner of bag.
Do not remove cookies from cookie sheet. Pipe candy coating over cookies. Before candy coating sets, sprinkle candy mixture over cookies. Place cookies to cooling racks. Cool completely, about 30 minutes.