Cover the buttered pie pan with the puff pastry, rolled out 1/6-inch thick, allowing for a margin of 1/2 to 3/4 inch beyond the edge. Sift the sugar, flour and powdered almond together, add the very softened butter, work with a whisk, adding 2 eggs one by one until white. Add the rum then the charm. Pour this cream into the pastry. Make a 1/8-inch thick lid with the remaining pastry. Brush the edges of the pastry in the pan with the beaten egg, cover with the lid. Roll the covered pie only once with the rolling pin. Leave to settle in the refrigerator for at least 1 hour. When you wish to bake, work the 1/2 egg white with as much icing sugar sifted with flour as possible to make a dough. Spread thinly over the cake, using a soft spatula. With the remaining puff pastry, rolled out in an 1/8-inch thick rectangle, cut ribbons, use to make a crisscross lattice topping the pie. Prick the lid here and there. Bake in a hot oven (425F) for 20 minutes without opening, then turn down to 350F. If necessary, cover with a paper if already golden brown and bake for a further 30 to 35 minutes. Open the oven, wait for a few minutes before taking out the pie. Allow to cool on the cake rack.
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For a 10-inch cake:
1 lb puff pastry, rolled out 4 times, or 2 packs deep-frozen puff pastry
