Beat butter at medium speed with an electric mixer until creamy. Add 2/3 cup powdered sugar, 1 teaspoon peppermint extract, and salt; beat well. Gradually add flour to butter mixture, beating at low speed just until blended after each addition. Divide dough into thirds; cover and chill 30 minutes.
Working with 1 portion of dough at a time, divide each portion into 12 pieces. Roll each piece into a 2-inch log; curve ends of each log to form a crescent. Place crescents 2 inches apart on lightly greased baking sheets.
Bake at 325 degrees for 18 minutes or until lightly browned. Cool 1 minute on baking sheets. Carefully roll warm cookies in 1 cup powdered sugar, and then cool completely on wire racks.
Combine remaining 1 cup powdered sugar, milk, and 1/4 teaspoon peppermint extract, stirring until smooth. Drizzle icing over cookies; sprinkle with crushed peppermint, pressing gently. Let icing set before serving. Store cookies in an airtight container.
Yield: 3 dozen.
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