Preheat oven to 350 degrees F.
In the bowl of a stand mixer or using a hand-held mixer, mix the butter and cornstarch until well combined and lighter in color.
Turn mixer off and add in confectioners sugar.
With the mixer on low, and the peppermint extract and mix until ingredients are fully incorporated.
Turn mixer off and add flour. With the mixer on low to medium-low, mix until the dough comes together (pulls away from sides of the bowl).
Using a 1 tablespoon cookie scoop, (you can also use a tablespoon measuring spoon) remove about a tablespoon of dough. Place on parchment lined cookie sheet at least 2 inches apart. (for a standard cookie sheet you can fit at least 8 cookies, a larger cookie sheet can hold about 14)
Once the cookie sheet is full, gently roll each between your hands until it is a smooth ball.
Bake 9 minutes.
Right out of the oven take a glass with a flat bottom (that is smaller than the cookie) and gently press into the cookie.
10. Allow cookies to cool for about 5 minutes and then move to a cooling rack. Make sure cookies are completely cool before adding glaze.