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 large mixing bowl, cream the softened unsalted butter and granulated sugar together using an electric mixer on medium speed until light and fluffy, about 3 minutes.
Add the vanilla extract and salt to the butter mixture and mix until combined.
Gradually add the all-purpose flour to the butter mixture, mixing on low speed until the dough just comes together. Do not overmix.
Transfer the dough to the prepared sheet pan. Use your hands or a spatula to press the dough evenly and firmly into the pan, smoothing the surface.
Using a sharp knife, score the dough into 24 equal squares to make cutting easier after baking.
Prick the surface of the dough evenly with a fork to prevent puffing during baking.
Bake in the preheated oven for 25 minutes, or until the edges are lightly golden but the center is still pale.
Remove the sheet pan from the oven and allow the shortbread to cool completely in the pan on a wire rack.
Once cooled, carefully lift the shortbread out of the pan using the parchment paper overhang and cut along the scored lines to separate the cookies.
Store the shortbread cookies in an airtight container at room temperature for up to 1 week.