To make the frangipane filling: Place almond paste into a food processor or blender with about half of the sugar, and process until well blended. Add butter and remaining sugar and process until smooth; blend in 1 egg, vanilla extract, almond extract, flour and salt. Set aside.

Preheat the oven to 425 degrees F (220 degrees C). Line a baking sheet with parchment paper; set aside.

Roll out one sheet of puff pastry into an 11-inch square. Keep pastry cool, trying not to knead or stretch it. Use a large pie plate, cake pan, or skillet to trace an 11-inch circle onto the dough using the tip of a small knife. Place the circle of pastry onto the prepared baking sheet. Repeat with the second sheet of pastry; place on a plate. Refrigerate both sheets.

Mound almond frangipane filling onto the center of the pastry that is on the baking sheet. Leave about 1 1/2 inch margin at the edges. Press the bean or fève down into the filling. Place the second sheet of pastry on top, and press down the edges to seal. Beat the remaining egg with a fork, and lightly brush onto the top of the galette. Use a knife to make a crisscross pattern in the egg wash, and then prick several small slits in the top to vent steam while baking.

Bake for 15 minutes in the preheated oven. Do not open the oven until the time is up, as the pastry will not fully puff. Remove from the oven, and dust with confectioners' sugar. Return to the oven, and cook for an additional 12 to 15 minutes, or until the top is a deep golden brown. Transfer to a wire rack to cool.

Lay a golden paper crown gently on top of the cake. This will be used to crown the person who finds the bean or fève. Serve warm or cold.