Preheat oven to 350 degrees F.
In a large bowl at low speed, beat butter until creamy looking. Add powdered sugar; mix until light and fluffy. Add peppermint extract; beat well. Add flour and cornstarch into butter mixture and mix well until well combined.NOTE: At first the dough will look dry - but don't worry, as the dough slowly comes together as you mix it and the butter melts into the dry ingredients.
Do not refrigerate this dough, as the butter will harden and make the dough unmanageable for rolling to a ball.
Using your hands, roll cookie dough into 1-inch balls. Place onto ungreased cookie sheets and bake approximately 12 to 15 minutes or until bottoms are light brown. Remove from oven, carefully remove from baking sheet, and cool on wire cooling racks (when warm the cookies are delicate).
When cookies have cooled, spread Peppermint Frosting onto top of cookies. Immediately sprinkle the crushed peppermint candies over the tops.
Store in an airtight container.
In a medium bowl, combine butter, peppermint extract, food coloring (if desired), and powdered sugar; stir until well mixed. NOTE: Additional milk may be needed to get the frosting thin enough.
NOTE: After making many batches of Peppermint Frosting, I now thin the frosting with additional milk or water and dip the top of the cookie into it. This technique is much faster and easier.
Peppermint Melt Away Cookie Recipe: https://whatscookingamerica.net/cookie/pepperminmeltawaycookie.htm