Preheat oven to 275°. Butter a 9 x 13 x 1 inch baking pan and line the bottom with parchment paper.
In the bowl of an electric mixer, cream the butter and sugar on medium speed until a light and fluffy mixture forms (about 2 minutes). Add the salt and vanilla and beat just to combine. Add flour, 1 cup at a time, beating on low speed, until just combined.
Press dough into the prepared pan, leveling and smoothing the top (I just use my palms to do this). Using a dough scraper or a small sharp knife, cut dough lengthwise into nine strips (slightly less than an inch each). Cut the strips crosswise into thirty six 3 inch bars. Using the tines of a for, create a decorative pattern on the surface.
Bake shortbread until evenly pale golden, but not too browned (about 70-85 minutes). Transfer pan to a wire rack to cool. Carefully cut the bars with a serrated knife. Store in an airtight container for up to one month. They also freeze very well.