Cornmeal Lemon Shortbread Cookies

Source: Une Gamine Dans la Cuisine
(recipe : Dorie Greenspan's
(Baking, From My Home to Yours)

1-1/2 cups all-purpose flour
1/4 cup cornstarch
1/2 teaspoon salt
1/2 cup yellow cornmeal
2/3 cup sugar
Grated zest of 1 lemon
2 sticks (8 ounces) unsalted, room temperature butter
1 teaspoon of pure vanilla extract, or 1/2 teaspoon of pure almond extract

In a medium size bowl, sift together the flour, cornstarch, and salt. Whisk in the cornmeal, and set the mixture aside.
Working in the bowl of a stand mixer or other large bowl, rub the sugar and zest together with your fingertips until the sugar is moist and fragrant.
Add the butter and extract to the bowl and, using either your stand mixers paddle attachment or whisk, or a hand mixer, beat on medium speed until the mixture is very smooth (about 3 minutes).
Reduce the mixer to low speed and add the dry ingredients, mixing only until the flour streaks have disappeared into the dough (do not over-mix).
Using a rubber spatula, transfer the dough (which will be soft and sticky) into a gallon-size zipper-lock plastic bag.
Leaving the top open, place the bag on a flat surface and roll the dough into a 9 x 10 1/2-inch rectangle that's about 1/4-inch thick. Be sure you don't roll all the way to the open end of the bag, you want to still be able to close it. As you are rolling the dough, turn the bag occasionally to prevent creasing.
Pressing out as much air as possible, seal the bag and refrigerate the dough for at least 2 hours. The sealed dough will keep for up to 2 days in the refrigerator.

Getting ready to bake:
Position the racks to divide the oven into thirds. Preheat the oven to 350F, and line two baking sheets with parchment paper or silplat mats.
Place the dough-filled plastic bag on a cutting board, slit it open, and discard the bag. Using a ruler as a guide and a sharp knife, cut the dough into 1 1/2-inch squares. Transfer the squares to the prepared baking sheets and carefully prick each one twice with a fork (be sure the tines go all the way through to the baking sheet).
Place the baking sheets in the oven and immediately lower the oven temperature to 300F. Bake the cookies for 25-30 minutes, rotating the sheets from top to bottom and front to back halfway through the baking time. The cookies should be set and just slightly golden.
Transfer the cookies to a cooling rack and cool to room temperature.