Position a rack in the middle of the oven and heat the oven to 325 degrees F. Lightly grease the sides and bottom of a 9x13-inch baking pan. Line the bottom of the pan with the parchment.

In a medium bowl, whisk the flour, cornnmeal, and salt to blend. In a large bowl, combine the butter, confectioners' sugar, lemon zest, and vanilla; with a hand-held electric mixer or a stand mixer fitted with the paddle attachment, beat on medium-high speed until light and creamy, 3 to 4 minutes. Scrape the bowl. Add the flour mixture and mix on low speed until the dough begins to form moist clumps. Dump the dough into the prepared pan.

Using a rubber spatula or lightly floured fingertips, spread the dough into the pan in a smooth, even layer. Dip the tip of a knife or a small metal spatula in flour (to prevent sticking) and score the dough all the way through into bars that measure 1x2-1/2 inches (about 1 inch across the short side and just a smidgen over 2-1/2 inches on the long side). Bake until the tops look dry and golden brown, 35 to 40 minutes. Transfer the pan to a rack. Immediately cut the shortbread into bars, with a metal bench scraper or a knife, using the scored lines as a guide (they will have faded a bit during baking). It's important to do this right after the shortbread comes out of the oven; if you wait until it has cooled, it will crumble when you try to cut it. Let the bars cool completely in the pan before removing them with a small, flexible offset spatula.

Make Ahead Tip: The shortbread dough can be pressed into the pan, scored, covered, and frozen up to a month before thawing and baking. The baked bars keep, well wrapped, for up to three days a room temperature.