Preheat oven to 350°F. Line an 8x8-inch baking dish with parchment paper.
In the bowl of a stand mixer with a paddle attachment, mix the flour, cornstarch, sugar, and salt at low speed until combined (about 5 seconds).
Cut the cold butter into ½-inch cubes. Place the butter cubes in a small bowl and toss with ¼ cup of the flour mixture.
Add the floured butter (with any extra flour) to the bowl of the stand mixer. Mix on low speed until the dough is a mixture of small crumbs (about 4 minutes).
Remove bowl from stand mixer and use your hands to toss the mixture and rub any remaining butter bits into the flour mixture.
Press the shortbread mixture firmly and evenly into the lined pan, smoothing it with the back of a spoon.
Bake 35-40 minutes, or until the top and edges are lightly golden brown.
Remove from the oven and let cool for about 5 minutes. (Leave the oven on for additional baking.)
After cooling, press a piece of parchment paper onto the shortbread. Cover the top with a sheet pan. Invert the shortbread upside down, and carefully lift off the pan, leaving the shortbread on the parchment paper on the sheet pan.
With a knife, slice the shortbread in half. Then, slice into fourths the other direction (giving you 8 rectangular cookies). Pierce a few holes on the top of each section with a toothpick, wooden skewer, or fork.
With the shortbread still on the parchment paper and baking sheet, bake an additional 8 minutes to firm up. Remove from oven and let cool before serving.