Mix in sifted cornstarch and flour until well combined.
Split soft dough in to 2 equal portions. Refrigerate for 2-3 hours.
Preheat oven to 375F. Line baking sheets with parchment paper.
Use a lightly floured surface (or powdered sugar, as adding too much flour can make the cookies too dense) and roll out the dough to 1/4 inch thickness. Use cookie cutters to cut out the desired shapes, then place them on baking sheet at least 1/2 inch apart.
Bake 15-20 minutes; they should be lightly browned around the edges. Let cool, before icing!