Cream together softened butter and confectioners' sugar until light and fluffy.

Blend in peppermint extract evenly into the batter.

Sift together flour, cornstarch, and salt in a separate bowl.

Gradually fold dry ingredients into butter mixture until just incorporated.

Form small 1-inch balls and place them on an ungreased baking sheet, spacing them 2 inches apart.

Preheat oven to 350°F (175°C) and bake cookies for 10-12 minutes until set.

Cool cookies completely on a wire rack.

Prepare frosting by combining butter, confectioners' sugar, milk, and peppermint extract; beat to smooth consistency.

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