In the bowl of a stand mixer fitted with a paddle attachment, cream together the butter and sugar until light and fluffy, about 3-5 minutes on medium speed. Add in the salt and vanilla extract, beat until combined. Mix in the beaten egg until everything comes together, scraping down the sides of the bowl as needed. Add in 1/2 of the flour and mix on low until the mixture begins to pull together. Add in the other 1/2 of the flour and mix on low until just almost combined. Remove the bowl from the stand and continue to incorporate the flour with a rubber spatula or with a clean hand. Using your hands, form the dough into a ball. Place on a piece of plastic wrap and flatten the ball into a disc about 1 inch high. Wrap tightly. Using a rolling pin, gently press on the dough to seal it tighter in the plastic wrap. Allow to chill 1 hour to overnight.