Preheat oven to 400°F. Unfold pastry sheet onto a lightly floured work surface. Combine cheese, zest and pepper in a small bowl. Sprinkle mixture over half of pastry sheet, leaving a 1/4-inch border. Fold other half over cheese mixture. Flour a rolling pin and roll pastry to a 14-by-7-inch rectangle. Cut crosswise into 3/8 -inch strips.
Twist each strip 4 or 5 times. Place on 2 ungreased baking sheets, pressing down on ends to keep strips twisted. Bake until golden brown (rotate pans halfway through), 11 to 13 minutes. Let cool on pan for 2 minutes. Remove straws; set aside until fully cooled. (Cheese straws will keep for several days in an airtight container.)