In a medium bowl, cream together the butter and 2/3 cup of sugar until light and fluffy. Stir in the flour salt and rosemary until well blended. The dough will be somewhat soft. Cover and refrigerate for 1 hour.
Preheat the oven to 375 degrees F (190 degrees F). Line cookie sheets with parchment paper.
On a lightly floured surface, roll the dough out to 1/4 inch thickness. Cut into rectangles 1 1/2x2 inches in size. Place cookies 1 inch apart on the lined cookie sheets. Sprinkle the remaining sugar over the tops.
Bake for 8 minutes in the preheated oven, or until golden at the edges. Cool on wire racks, and store in an airtight container at room temperature.