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.