Preheat the oven to 325°F (163°C). Line an 8-inch square baking pan with parchment paper, leaving an overhang on the sides for easy removal.
In a large mixing bowl, cream together the softened unsalted butter and granulated sugar until light and fluffy, about 3-4 minutes using an electric mixer on medium speed.
Add the pure vanilla extract and mix until combined.
In a separate bowl, whisk together the all-purpose flour and salt.
Gradually add the flour mixture to the butter mixture, mixing on low speed until just combined and a dough forms. Do not overmix.
Press the dough evenly into the prepared baking pan, smoothing the top with the back of a spoon or your fingers.
Using a sharp knife, score the dough into 24 squares, cutting all the way through to the bottom of the pan.
Prick each square several times 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 centers remain pale.
Remove from the oven and allow the shortbread to cool completely in the pan on a wire rack.
Once cooled, lift the parchment paper to remove the shortbread from the pan and cut along the scored lines to separate the squares.
Store the shortbread cookie squares in an airtight container at room temperature for up to one week.