In a large mixing bowl, combine one cup of softened unsalted butter with two cups of confectioners' sugar. Use an electric mixer on medium speed to blend until light and fluffy, about 3-5 minutes.

Mix in one teaspoon of pure peppermint extract until fully incorporated.

In a separate bowl, whisk together two cups of all-purpose flour, half a cup of cornstarch, and a pinch of salt. Gradually add this to the wet mixture, mixing on low speed.

Wrap the dough tightly in plastic wrap and refrigerate for at least 30 minutes.

Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

Remove the dough from the refrigerator and roll it into small balls, about one inch in diameter, placing them 1-2 inches apart on the baking sheet.

Bake for 10-12 minutes, until set but not browned. Allow to cool on the baking sheet for a few minutes before transferring to a wire rack.

Make the frosting by beating together half a cup of softened butter, three cups of confectioners' sugar, 2 tablespoons of milk, and one teaspoon of peppermint extract until smooth.

Spread or pipe the frosting onto each cooled cookie.

Sprinkle crushed peppermint candies on top of the frosted cookies.