Preheat oven to 375 degrees F.
On a floured surface, roll the pastry out a little thinner than 1/8-inch. Lay on a sheet pan and chill it, then cut out 4-inch disks. Cut decorative shapes from the scrap and bake them off to use later.
Slice peeled, halved, and cored apples extremely thinly, preferably on a mandoline.
In a small bowl, mix the cinnamon and sugar together.
Lay pastry disks on a parchment lined sheet pan and place 1 cube of butter in the center on each puff pastry disk and a spoonful of cinnamon sugar. Start layering and stacking the apple slices in a concentric circle leaving very little edge showing to make a beehive shape (save the smaller slices for the top layers). It should get smaller as you go up higher.
When finished, the stack of apple layers should be about 3 inches high. Place a cube of butter at the top and sprinkle the apple stack liberally with cinnamon sugar. You can freeze them at this point. Bake until golden brown and tender, about 30 minutes.
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