Sprinkle work surface lightly with granulated sugar. Lay one sheet of puff pastry flat on surface and sprinkle evenly with about 3 tablespoons sugar. Beginning at one side, fold in dough, 1/2 inch at a time, to the center of the square. Repeat to fold in the other side so the two rolls are touching.
With a sharp knife, cut roll crosswise into 1/4- to 1/2-inch-thick slices. Lay cookies flat, 1 inch apart, on buttered 12- by 15-inch baking sheets. Repeat to fold and slice remaining sheet of puff pastry; arrange cookies on baking sheets. Sprinkle cookies generously with large-crystal decorating sugar (or more granulated sugar).
Bake cookies in a 375° regular or convection oven until golden brown all over, 18 to 22 minutes; if baking more than one sheet at a time in one oven, switch positions halfway through baking. Transfer palmiers to racks to cool completely.
Nutritional analysis per cookie.