In a large bowl cream together the butter and sugar until light and fluffy, using a hand beater. Beat in the egg and then the vanilla. In a separate bowl, combine the flour and salt. Stir the dry ingredients into the wet ingredients until just incorporated. Roll the dough into a log, on a work surface, wrap in parchment and chill in the refrigerator for at least 1 hour. Put 2 cookie sheets in the refrigerator to chill as well.
Preheat the oven to 400 degrees F.
Remove the chilled dough from the refrigerator and slice into 1/4-inch rounds. Arrange 2 inches apart on the chilled cookie sheets and bake until lightly golden on the edges, about 8 to 10 minutes. Remove the cookies from the cookie sheets and put on a cooling rack to cool before serving.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.