In a small bowl, whisk the flour, salt, lemon zest, and rosemary. Set aside.
In the bowl of a stand mixer, beat the butter and powdered sugar until smooth and creamy, about 3 minutes. Beat in the vanilla extract and lemon juice. Slowly add in the flour mixture and mix until just combined. Form the dough into a disk shape and wrap in plastic wrap. Chill the dough for at least 1 hour or until firm.
When ready to bake, preheat oven to 325 degrees F. Line a large baking sheet with parchment paper or a Silpat and set aside.
On a lightly floured surface, roll out the dough into a 1/4 inch thick square. Cut into squares, rounds, or shape of your choice using a lightly floured cookie cutter. Place shortbread cookies on the prepared baking sheet and bake for 10-12 minutes, or until cookies are very lightly browned around the edges. Remove cookies from baking sheet and cool completely on a wire rack.
Note-Shortbread cookies with keep in an airtight container for about a week or they can be frozen.