In a medium bowl, beat the butter at medium speed with an electric mixer until creamy; gradually add the sugar, beating well. Gradually add the flour to the butter mixture, beating at low speed until blended. Gently stir in the rosemary.
Use your hands to mold the dough into a ball. Roll the dough to ¼-inch thickness on a lightly floured surface. Cut with a 2-inch cookie cutter of any shape; place the cutouts on lightly greased baking sheets (or parchment-lined).
Bake for 16 to 18 minutes or until the edges are lightly browned. Remove the cookies to wire racks to cool completely.
Notes
These are great with a cup of tea, or atop a scoop of sherbet.