Roll out one puff pastry sheet to a 1/4-inch thick rectangle 10″ x 12″. Spread half of the softened butter on the pastry and sprinkle with half of the remaining cinnamon-sugar mixture.
Roll up the pastry from the long end. Cut equally into two shorter logs, and cut each of those in half lengthwise. Coil each piece around your finger and pinch the ends to seal. Repeat with the other sheet of pastry.
Place the shaped pastries in the prepared pan, and bake 20 to 25 minutes. Sprinkle with the remaining cinnamon-sugar when you take them out of the oven.