Roll out puff pastry dough into a rectangle 20 by 24 inches. Sprinkle half of the Parmesan evenly over the dough and gently press cheese into the dough with the rolling pin.
Fold the dough in half crosswise, roll it out again to 20 by 24 inches, and sprinkle on remaining cheese.
Using a sharp thin knife, cut the dough into 1/3-inch strips. Take each strip by its end 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 in the middle of a preheated 350F oven and bake until the straws are crisp, puffed brown, 15 to 20 minutes.
Remove from the oven, cool for 5 minutes, then cut apart with a sharp knife. Finish cooling the straws on a rtack, then store them in an airtight tin or plastic bag until serving time. They will stay fresh for about 1 week. About 20 straws. Arrange a basketful on the bar when entertaining and watch them disappear!