Preheat the oven to 400 degrees F.
Combine the sugar, cinnamon, and orange zest in a bowl. Sprinkle 1/2 the sugar mix on a clean work surface. Lay the puff pastry on top of the sugar and sprinkle the remaining sugar mix on top of the pastry.
Using a rolling pin, roll the sugar into the dough, and roll the dough into an even rectangle, about 1/8-inch thick.
Working from the short ends of the rectangle, roll up each end of the dough to meet in the middle. Lay the rolls on top of each other and gently press to secure. Wrap the dough in plastic and let sit in the refrigerator for at least 30 minutes.
Cut the dough into slices that are 1/4-inch thick. Lay the slices on 2 parchment paper or silpat-lined sheet trays and bake in the preheated oven for 12 minutes. Turn the slices over and bake for another 6 to 7 minutes. When done, the cookies should be golden brown.
Remove from the oven, and cool on a rack before serving.