In the bowl of an electric mixer fitted with a paddle attachment, mix together the butter and sugar until combined. Add the vanilla and mix to combine.

In a separate bowl, add the flour, cornstarch, and salt and whisk to combine. Add the flour mixture to the butter mixture and mix on low until flour is incorporated. Do not over-mix. Transfer the dough to a work surface dusted with flour. Shape the dough into two round disks about 1/2-inch thick. Wrap the disks in plastic and refrigerate for at least 1 hour or overnight.

Pre-heat the oven to 350 degrees f. Line a baking sheet with parchment paper or a silpat.

Using 1 dough disk at a time, roll the dough out on a lightly floured surface about 1/4 to 1/3-inch thick. Cut cookies using a cookie cutter or biscuit cutter. Transfer cut cookies to the baking sheet. Bake for 15 to 20 minutes, or until the edges are slightly brown. Remove the cookies from the oven and wait 1 minute before transferring cookies to a cooling rack. Allow the baking sheet to cool completely between batches. Store cookies in a sealed container.