Beat butter at medium speed with an electric mixer until creamy. Gradually add 2/3 cup powdered sugar, 1 teaspoon peppermint extract, and salt, beating well. Gradually add flour, beating until blended.
Divide dough into 3 portions; divide each portion into 12 pieces. Roll each piece into a 2-inch log, curving ends to form a crescent. Place crescents 2 inches apart on lightly greased baking sheets.
Bake at 325° for 15 to 18 minutes or until lightly browned. Cool 5 minutes. Carefully roll warm cookies in sifted powdered sugar. Cool completely on wire racks.
Stir together milk, remaining 1 cup powdered sugar, and remaining 1/4 teaspoon extract until smooth. Drizzle cookies with icing, and sprinkle with crushed candies, gently pressing. Store in airtight containers.