In a large mixing bowl, use an electric mixer to cream together 1 cup of softened unsalted butter and 1 cup of confectioners' sugar until light and fluffy, about 3-5 minutes.

Slowly add in 1 teaspoon of peppermint extract, mixing until fully incorporated. Scrape down the sides of the bowl.

In a separate bowl, whisk together 2 cups of all-purpose flour, 1/4 cup of cornstarch, and 1/4 teaspoon of salt until well blended.

Gradually incorporate the dry mix into the wet ingredients to form a smooth dough.

Shape the dough into small balls, about 1 inch in diameter, and roll in confectioners' sugar. Place on lined baking sheet.

Cover with plastic wrap and chill in the refrigerator for at least 30 minutes.

Preheat oven to 350°F (175°C). Bake cookies for 10-12 minutes until set but not browned.

Cool on the baking sheet for about 5 minutes, then transfer to a wire rack.

In a medium bowl, beat together 1/4 cup softened butter and 1 cup confectioners' sugar until creamy. Gradually mix in 2 tablespoons milk, 1 teaspoon peppermint extract, and food coloring until smooth.

Frost cooled cookies and sprinkle with crushed peppermint candies. Allow frosting to set before serving.