In the work bowl of a stand mixer fitted with the paddle attachment - Add the butter and sugar and beat on medium speed until light an fluffy. Add the egg yolk and vanilla extract and beat until incorporated - scraping down the sides of the bowl as needed.
Turn the mixer down to low speed and sprinkle in the salt, then flour in a few increments - letting the flour mix in before adding the next increment. Scrape down the sides of the bowl as needed. After adding the last increment of flour, let the dough mix for about a minute until it starts to form a rough dough. The dough will be crumbly.
Turn off the mixer and gently knead the dough together with your hands until it forms a ball. Place the dough ball on a piece of plastic wrap and shape it into a 6 inch round log. Tightly wrap it with the plastic wrap and continue to form the log shape by rolling the dough on the counter to get the round shape. Refrigerate the dough log for at least two hours, or overnight. We want it to be nice and chilled to slice and bake it. You can also freeze it.
15 minutes before you are ready to slice and bake the cookies - preheat the oven to 350F degrees and adjust the oven rack to the middle position. Line two baking sheets with parchment paper.
Using a sharp chef's knife, slice the chilled dough log into (at least) 1/4 inch thick cookies. Place the cookies 2 inches apart on the prepared baking sheets.
One baking sheet at a time - bake the cookies for 9-12 minutes, or until the edges just start to golden. High altitude - check the cookies at 9 minutes as they may not take as long to bake. Note - while the first baking sheet of cookies are baking, refrigerate the other baking sheet of cookies until ready.
Cool the cookies on the baking sheet set on a wire cooling rack for 5 minutes, then transfer to the cooling rack to cool completely.