Preheat the oven to 350°. In a food processor, combine the flour, sugar and salt. Add the butter and vanilla and pulse until evenly moistened. Turn the crumbs out onto a large piece of parchment paper and press into a disk.
Cover with another sheet of parchment paper and roll out the dough to a rough 8-by-11-inch rectangle. Discard the top sheet of parchment. Trim the edges to form a 7-by-10-inch rectangle. Slide the dough along with the parchment onto a large baking sheet. Using a straight edge and a sharp knife, score the dough into 24 bars. Poke the dough all over with a fork and freeze until firm, about 10 minutes.
Bake the dough until golden, about 25 minutes. While the shortbread is still warm, cut it into bars. Let cool before serving.
The shortbread can be stored in an airtight container for up to 1 week.