In a large bowl, combine the flour, cornmeal and salt. Cut in shortening until mixture resembles coarse crumbs. Stir in cheddar cheese. Sprinkle with 1/3 cup water. Toss with a fork (if dough is dry, add water, 1 teaspoon at a time, until dough forms a ball). Wrap tightly in plastic wrap; refrigerate for 1 hour or until firm.
Divide dough in half. On a lightly floured surface, roll each portion into an 11-in. x 10-in. rectangle. Cut into 5-in. x 1/2-in. strips. Carefully twist each strip and place on greased baking sheets, pressing ends down.
Bake at 425 degrees F for 7-9 minutes or until golden brown. Immediately sprinkle twists with Parmesan cheese. Cool on wire racks. Store in an airtight container.