To begin, to a small bowl add your flour, cornstarch and salt and whisk them together gently.
To a large mixing bowl, add your butter and sugar and beat them together till creamy. Add your egg white and peppermint extract and briefly blend in. Add your dry ingredients and mix together till you have smooth cookie dough.
Cover your bowl and place it in your fridge to chill for at least on hour. At one hour, check the cookie dough texture. It should be somewhat firm but still easy to scoop out. *If you aren't sure if your dough has chilled long enough, bake only one cookie (and if it spreads too thin, your dough needs to chill longer!).
Preheat your oven to 350 and line a pan with parchment paper, or spray with non-stick spray. Scoop your cookies out onto your pan, evenly spaced apart, with no more than 12 cookies per pan. Bake in the oven for 12-14 minutes, or till the edges of the cookies are set and just starting to turn a light golden color.
Let your cookies cool entirely before adding the glaze on top.
To a small mixing bowl, add your powdered sugar, milk and peppermint extract and whisk thoroughly till well combined. Add a little more milk if it's too thick.
Holding each cookie upside down, dip the top into the bowl of glaze, then place on top of a cooling rack (so the extra glaze drains off instead of making the bottom of the cookies soggy). Immediately sprinkle crushed up candy canes on top.
Stored in an airtight container these cookies are best within the first 5 days.