Roll puff pastry into a 12 by 15-inch rectangle. Spread pesto evenly over pastry, to within 1/8-inch of the edges. Fold dough in half lengthwise. Roll dough out again into a 12 by 5-inch rectangle. Sprinkle Parmesan over new rectangle. Cut dough crosswise into 1/2-inch thick strips. Twist each strip into a corkscrew. Arrange twists on a large baking sheet and press down ends to prevent unrolling. Bake 10 minutes, until puffed up and golden brown.