Cream the softened butter and confectioners' sugar in a large bowl for 3-4 minutes until the mixture is noticeably lighter in color and fluffy. Beat in the peppermint extract until well combined.

In a separate bowl, whisk together flour, cornstarch, and salt. Gradually add this dry mixture to the creamed butter, mixing just until no flour streaks remain.

Cover the dough with plastic wrap and chill for at least 30 minutes until firm but not rock-hard.

Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper. Shape the chilled dough into 1-inch balls and place them 2 inches apart on prepared sheets.

Bake for 9-11 minutes or until the bottoms are lightly golden brown. The tops should remain pale white. Cool on baking sheets for 5 minutes, then transfer to wire racks and cool completely (about 30 minutes) before frosting.

For the frosting, beat 2 tablespoons of butter until creamy, then gradually add confectioners' sugar, milk, peppermint extract, and food coloring. Beat until smooth and spreadable. Spread over cooled cookies and sprinkle with crushed peppermint candies.