In a large bowl, combine flour, powdered sugar, and cornstarch. Whisk to combine.
Add your softened butter to the dry ingredients. Using your hands or a utensil (fork or pastry cutter), mix everything together until the butter breaks up and absorbs the dry ingredients. You should be left with a soft ball and sticky dough.
Transfer the dough onto a piece of plastic wrap and flatten into a rough disk shape. Wrap and chill in the fridge for 1 hour, or until firm.
Preheat your oven to 325°F. Line a large baking sheet with parchment paper, and set aside.
Turn your chilled dough onto a lightly floured work surface. Roll the dough out into about a 1/4 inch thick (you can go thicker if you like - the bake time will be slightly longer). Cut out your desired shapes using a sharp knife, pizza cutter, or cookie cutter. I just went with simple rectangle cutouts.
Arrange the cookies on your parchment lined baking sheet, leaving about an inch of space between each cookie. (Optional) Use a skewer or fork to poke holes on the surface for a classic look.
Bake the cookies in your preheated 325°F oven for 15 to 20 minutes. The cookies should be just barely golden brown on the edges and bottom, with a matte finish on top. Cool the cookies for 5 minutes on your baking sheet before transferring to a wire cooling rack to cool completely to room temperature. They will harden once cooled.