In a bowl, whisk together the all-purpose flour, sifted corn starch, powdered sugar and salt. Set aside.
Beat butter and vanilla in a mixer. Add flour mixture slowly and combine.
Form it into a ball on plastic wrap and press it into about a 2-inch round. Wrap it tightly in plastic wrap and transfer to the fridge to chill for about 30 mins.
Preheat the oven to 350 degrees F.
Transfer the dough to the center of a sheet of parchment. Place a sheet of parchment on top and roll it out slowly. Roll it out 1/2 to 1/4-inch thick.
Using a 2-inch cookie cutter, cut out cookies. Transfer to parchment-lined baking sheet and bake 11-13 mins. Cool.