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 bowl, beat the softened unsalted butter and granulated sugar together using an electric mixer on medium speed until light and fluffy, about 3-4 minutes.
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 soft dough forms.
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 about halfway through the dough but not all the way to the bottom.
Prick each square a few 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 center is still pale.
Remove from the oven and allow the shortbread to cool completely in the pan on a wire rack.
Once cooled, use the parchment paper overhang to lift the shortbread out of the pan and cut fully along the scored lines to separate the squares.
Store the shortbread cookie squares in an airtight container at room temperature for up to 1 week.