Roll out the puff pastry dough into a rectangle 20 × 24inches. Sprinkle half of the cheese evenly over the dough and gently press the cheese into the dough with the rolling pin.
Fold the dough in half crosswise, roll it out again to 20 × 24inches, and sprinkle on the remaining cheese.
Using a sharp thin knife, cut the dough into ⅓-inch-wide strips. Take each strip by its ends and twist until evenly corkscrewed. Lay the twists of dough on an ungreased baking sheet, arranged so they are just touching each other; this will prevent untwisting.
Set the baking sheet on the center rack of the oven and bake until the straws are crisp, puffed, and brown, 15 to 20 minutes.
Remove the straws from the oven, cool for 5 minutes, then cut them apart with a sharp knife. Finish cooling the straws on a rack, then store them in an airtight tin or plastic bag until serving time. They will stay fresh for about 1 week.