Preheat the oven to 325 degrees Fahrenheit. Line two baking sheets with parchment paper and set aside.
Combine the flour, salt and rosemary in a food processor and pulse a few times until well blended and the rosemary is evenly dispersed.
In a stand up mixer combine butter and powdered sugar. Beat until light and fluffy, scraping down the sides as needed. Add vanilla and flour mixture and mix until it [i]just[/i] starts to come together.
Turn dough onto a flour surface and bring together with hands. Roll out between two pieces of parchment paper to about 1/4". Place the dough in the refrigerator for 30 minutes, until firm.
Using a cutter, cut out cookies and place them on the prepared baking sheets. Return to the refrigerator for 20 more minutes.
Baking for 16-20 minutes until the edges begin to turn golden brown. Remove from oven and let cool for 3 minutes before transferring to a wire cooling rack to cool completely.