Beat butter at medium speed of an electric mixer until creamy; gradually add powdered sugar and cornstarch, beating well. Stir in flour and rosemary. (Dough will be stiff.)
Divide dough in half. Shape 1 portion of dough into a 6 1/2" circle on an ungreased cookie sheet. Crimp edges with a fork. Cut dough into 8 wedges (do not separate). Repeat procedure with remaining dough. Cover and chill 1 hour.
Bake at 300° for 30 minutes or until done. Cool on cookie sheet 5 minutes. Remove shortbread wedges to a wire rack, and cool completely.