In a large mixing bowl, using an electric mixer, cream together the softened unsalted butter and granulated sugar on medium speed until light and fluffy, about 2-3 minutes. Scrape down the sides of the bowl as needed. Add the vanilla extract, if using, and mix until just combined.

In a separate medium bowl, whisk together the all-purpose flour, cornstarch, and salt. Gradually add the dry ingredients to the butter mixture, mixing on low speed until just combined and a soft, crumbly dough forms. Be careful not to overmix, as this can make the shortbread tough.

Gather the dough together with your hands and gently press it into a disk. Wrap the dough tightly in plastic wrap and refrigerate for at least 30 minutes (or up to 2 days). This chilling step is crucial for preventing the cookies from spreading and ensures a better texture.

Preheat your oven to 325°F (160°C). Line two large baking sheets with parchment paper.

On a lightly floured surface, or between two sheets of parchment paper, roll out the chilled dough to a thickness of about 1/4 to 1/3 inch (6-8mm). Use cookie cutters to cut out desired shapes, or simply cut the dough into rectangles or rounds with a knife.

Carefully transfer the cut-out cookies to the prepared baking sheets, leaving about 1 inch between them. Prick the tops of the cookies several times with a fork (this helps them bake evenly and gives them their classic appearance).

Bake for 15-20 minutes, or until the edges are lightly golden and the centers are set but still pale. Baking time may vary depending on the thickness and size of your cookies. Do not let them get too brown.

Remove the baking sheets from the oven and let the cookies cool on the sheets for 5-10 minutes before transferring them to a wire rack to cool completely.