01 - Whisk together flour, baking powder, and salt in a medium bowl, then set aside.
02 - Using an electric mixer, beat butter and granulated sugar in a large bowl until light and fluffy, about 2 minutes.
03 - Add egg, vanilla extract, and peppermint extract to the butter mixture and beat until thoroughly combined.
04 - Gradually add the flour mixture to the wet ingredients, mixing just until incorporated.
05 - Divide dough in half; tint one half with red food coloring and knead until color is even.
06 - On a lightly floured surface, roll each dough half into a 12-inch log. Twist the two logs together, then gently roll into a single log. Wrap tightly with plastic wrap and chill for at least 30 minutes.
07 - Heat oven to 350°F. Line two baking sheets with parchment paper.
08 - Cut chilled dough into 1/2-inch slices and space them 2 inches apart on the prepared baking sheets.
09 - Bake cookies for 10 to 12 minutes until edges are lightly golden. Cool on baking sheets for 2 minutes, then transfer to wire racks to cool completely.
10 - Beat unsalted butter until creamy. Gradually add powdered sugar, milk, peppermint extract, and salt, beating until smooth and spreadable.
11 - Spread frosting over cooled cookies and immediately sprinkle with crushed peppermint candies.