Cream butter in a large mixing bowl; set aside.
Combine flour, salt, mustard, and pepper in a large mixing bowl; mix well. Add 2 cups flour mixture to butter; beat well. Gradually add cheese; beat well. Add remaining flour mixture; beat well.
Press dough onto greased baking sheets, using a cookie press fitted with a star disc. Bake at 350° for 10 minutes or until lightly browned. Store in airtight containers, placing waxed paper between layers.
Note: Cheese Straws may be frozen in airtight containers.