In a separate bowl whisk the flour with the salt. Set aside.
In the bowl of your electric mixer (or with a hand mixer), cream the butter until smooth (about 1 minute). Add the sugar and beat until smooth (about 2 minutes). Beat in the vanilla extract.
Gently stir in the flour mixture just until incorporated.
Flatten the dough into a disk shape, wrap in plastic wrap, and chill the dough for at least an hour.
Preheat the oven to 350 degrees F (177 degrees C) with the rack in the middle of the oven. Line two baking sheets with parchment paper.
On a lightly floured surface roll out the dough to ¼ inch (.5 cm) thick. Cut into rounds or whatever shapes you wish using a lightly floured cookie cutter.
Place the cookies on the prepared baking sheet and place in the refrigerator for about 15 minutes. This will firm up the dough so the cookies will maintain their shape when baked.
Bake for 8 – 10 minutes, or until cookies are lightly brown. Cool on rack.
Shortbread will keep in an airtight container for about a week or frozen for several months.
Makes about 20 shortbread cookies.