In a large bowl, with a mixer on medium speed, beat butter, ½ cup of sugar, flour, and cornstarch until smooth.
Evenly press dough into 2 cake pans (9-inches wide) with removable rims. Press edges of dough with fork tines to make a ridge pattern. Then, with fork tines, pierce dough all over in parallel lines 1 inch apart.
Bake in a 300°F oven until firm to touch and golden at edges, about 45 minutes. Sprinkle hot cookies with remaining 2 Tablespoons granulated sugar.
Cut each into 12 wedges. Cool on pan bottoms on racks.
Serve cookies, store them airtight up to 1 week, or freeze them to store longer.