Combine butter, sugar and egg in bowl; beat at medium speed until creamy. Add milk, vanilla and peppermint extract; continue beating until well mixed. Add flour and baking powder; beat at low speed until well mixed. Stir in crushed candy canes.
Divide dough in half; flatten each half slightly. Wrap each in plastic food wrap; refrigerate at least 2 hours or until firm.
Heat oven to 400ºF. Line cookie sheets with parchment paper; set aside.
Roll out dough, one-half at a time, on lightly floured surface (keeping remaining dough refrigerated) to 10x4-inch rectangle. Cut rectangle in half to make 2 (10x2-inch) rectangles. Make 1 1/4–inch wide cuts across both rectangles, creating 16 (2x1 1/4-inch) pieces. Place 1 inch apart onto prepared cookie sheets.
Bake 6-8 minutes or until edges are very lightly browned. Cool 1 minute on cookie sheets; remove to cooling rack. Cool completely. Set aside 16 cookies.
Line cookie sheets with parchment paper again. Melt candy coating as directed on package.
Spread bottom-side of 1 cookie with melted candy coating; immediately attach 2 candy canes, curved-side down. Turn over; carefully place onto prepared cookie sheets, repositioning candy canes, if necessary, to allow sled to sit level. Repeat with remaining cookies, candy coating and candy canes. Let stand until set.
Variation: Sparkling Sugar Cookies. Bake cookies as directed. Spread candy coating over top of each cookie. Immediately sprinkle each with white edible glitter or white sanding sugar.