Preheat the oven to 325°F (163°C). Line two baking sheets with parchment paper.
In a large mixing bowl, cream the softened unsalted butter and powdered sugar together using an electric mixer on medium speed until light and fluffy, about 3 to 4 minutes.
Add the vanilla extract and mix until combined.
Gradually add the sifted all-purpose flour and salt to the butter mixture, mixing on low speed until the dough just comes together. Do not overmix.
Turn the dough out onto a lightly floured surface and gently knead it a few times to bring it together.
Roll the dough out to about 1/4 inch (6 mm) thickness.
Use a 2-inch (5 cm) cookie cutter to cut out cookies and place them on the prepared baking sheets about 1 inch (2.5 cm) apart.
Gather the scraps, reroll, and cut out remaining cookies.
Optional: Prick the surface of each cookie lightly with a fork to prevent puffing.
Bake the cookies in the preheated oven for 20 to 25 minutes or until the edges are lightly golden.
Remove from the oven and allow the cookies to cool on the baking sheets for 5 minutes, then transfer them to a wire rack to cool completely.
Once cooled, store the shortbread cookies in an airtight tin container.