Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper.
Cream the butter and sugar until fluffy. In a separate bowl, mix the flour and cornstarch. Slowly add the flour mixture to the butter and sugar, and mix until blended. Roll out the dough to 1-inch thickness. Bake for 30 minutes or until lightly brown. Remove the oven and sprinkle with sugar on top while still warm. Cut into lengths, approximately 1 by 3-inches. Can be stored in an airtight container for up to 1 week.