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 the softened unsalted butter and granulated sugar together until light and fluffy, about 3 to 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 dough forms.
Press the dough evenly into the prepared baking pan, smoothing the top with the back of a spoon or your hands.
Using a sharp knife, score the dough into 24 equal squares, but do not cut all the way through.
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, lift the shortbread out using the parchment paper overhang 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.