Thaw the puff pastry if frozen. Roll one sheet of dough on a lightly floured work surface to 1/4-inch thick. Spread butter over surface of pastry.
Sprinkle with one half of the sugar. Roll second pastry sheet to the same size as first. Place on top of first. Sprinkle remaining sugar over whole surface.
Fold as sketched bringing the ends to within 3/4 inch of each other. Repeat this folding as shown.
Slice into 1/4-inch- thick "palm leaves". Put leaves on an ungreased baking sheet. Bake in a preheated 375 degree oven for 15 minutes. Turn cookies over with a spatula.
Continue baking until golden brown. Transfer palmiers on a rack to cool. Store in an airtight container.
