Line 3 baking sheets with parchment and dust 1 with flour. Using an electric mixer on low speed, beat together 2 cups flour, the butter, sugar, cornstarch and salt until the dough just comes together, about 2 minutes. Do not overbeat.
Transfer the dough to the floured baking sheet and press into an 8 1/2-inch square about 1/3 inch thick. Refrigerate until firm, about 30 minutes. Prick the dough all over with a fork. Cut into 1-by-1-inch squares and refrigerate until cold, about 15 minutes.
Position a rack in the center of the oven and preheat to 275 degrees . Divide the cookies among the remaining 2 prepared pans and bake 1 pan at a time, keeping the other refrigerated, until the bottoms of the cookies are golden, 30 to 35 minutes; let cool completely.