Line a baking sheet with parchment paper or a silicone baking mat.
In the bowl of an electric stand mixer fitted with the paddle attachment, add the butter and sugar and cream for about 2 - 3 minutes on medium speed until light and fluffy, and pale in color. Scrape down the sides and bottom the bowl half way through. Add in the vanilla and mix again.
Sift the flour and add the salt and then mix on low speed until they are combined and the dough starts to form clumps and pull away from the sides of the bowl (20 seconds to 1 minute).
With your hands, squeeze the shortbread dough together into a ball. Place onto some plastic wrap, flatten into a disc and put it in the fridge for 10 minutes.
Once chilled, roll out the dough on a lightly floured surface to about 1/4 of an inch thick. Try not to overwork the doughboy kneading it. Just press it gently together each time.
Once the dough is rolled out, use a 3 inch round or scalloped cookie cutter to cut out approximately 8-10 cookies. Place on the prepared baking tray.
Refrigerate the cookies for 30 minutes minimum.
Bake at 350°F for 10-12 minutes until the edges of the cookies are just starting to turn golden.
Remove from the oven, allow to cool on the baking sheet for 5-10 minutes, then transfer to a wire rack to cool completely.