On a floured surface, roll the puff pastry out a little thinner than 1/8-inch. Lay on a sheet pan and chill, then cut out 3 to 4-inch disks. Cut decorative shapes from the scraps and bake them off to use later.
Slice the apples extremely thin, preferably on a Japanese mandoline. In a small bowl, mix the cinnamon and sugar together. Lay pastry disks on a parchment-lined sheet pan and place one cube of butter and a spoonful of cinnamon sugar in the center on each puff pastry disk. Start layering and stacking the apple slices in a concentric circle leaving very little edge showing to make a bee hive shape (save the smaller slices for the top layers). The stack should get smaller as you go up higher. As you build, sprinkle some cinnamon sugar in between the layers occasionally. When you're finished, the stack of apple layers should be about 3-inches high. Place a cube of butter on the top and sprinkle the apple stack liberally with cinnamon sugar. You can freeze them at this point or bake at 375° till golden brown and tender, about 30 minutes.