In a medium mixing bowl, cream together ½ cup of softened butter and ½ cup of confectioners' sugar until smooth and fluffy, about 3-5 minutes.

Blend in 1 teaspoon of peppermint extract, then gradually add 1 cup of all-purpose flour, ½ cup of cornstarch, and a pinch of salt, mixing until combined.

Roll the dough into small balls, about 1 inch in diameter, and place them on an ungreased baking sheet, leaving about 2 inches of space between each.

Preheat your oven to 350°F (175°C). Bake the cookies for 10-12 minutes, until edges are lightly golden.

Allow the cookies to cool on the baking sheet for about 5 minutes, then transfer them to a wire rack to cool completely.

Beat 1½ cups of softened butter with 2 cups of confectioners' sugar until smooth. Gradually mix in 2 tablespoons of milk and 1 teaspoon of peppermint extract.

Spread frosting on each cooled cookie and sprinkle with crushed peppermint candies.