Pulse cheese and butter 3 or 4 times in a food processor until combined. Add flour and remaining ingredients; process 20 seconds or until mixture forms a ball and leaves sides of bowl. Roll with rolling pin to make a rectangle and 1/4 inch thick.
Use a cookie press fitted with a bar-shaped disk to shape dough into 2 1/2-inch straws. Or divide dough into fourths, and roll each portion into a 1/4-inch thick rectangle on floured wax paper. Cut into 2- X 1/2-inch strips with a knife or pastry wheel and twist the cheese straws. Place on ungreased baking sheets.
Bake at 375 F. for 8 to 10 minutes or until lightly browned. Transfer to wire racks to cool.