Preheat the oven to 325°F (163°C). Line a 9×13-inch sheet pan with parchment paper, leaving an overhang on the sides for easy removal.
In a medium bowl, whisk together the all-purpose flour, cornstarch, and salt until combined. Set aside.
In a large bowl, beat the softened unsalted butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3 to 4 minutes.
Add the vanilla extract to the butter mixture and mix until combined.
Gradually add the flour mixture to the butter mixture, mixing on low speed until just combined and a soft dough forms. Do not overmix.
Transfer the dough to the prepared sheet pan. Using your hands or an offset spatula, press the dough evenly into the pan, smoothing the surface.
Using a fork, prick the dough all over to prevent puffing during baking.
Bake in the preheated oven for 28 to 30 minutes, or until the edges are lightly golden and the center is set.
Remove from the oven and let the shortbread cool in the pan on a wire rack for 10 minutes.
While still warm, use a sharp knife to cut the shortbread into 24 squares or rectangles.
Allow the shortbread to cool completely in the pan before carefully lifting it out using the parchment paper.
Store the shortbread cookies in an airtight container at room temperature for up to 1 week.