Place almond paste into a food processor or blender with half of the sugar, and process until well blended. Add butter and remaining sugar and process until smooth. Blend in egg, vanilla extract, almond extract, flour, and salt. Set aside.

Preheat oven to 425°F (220°C). Line a baking sheet with parchment paper.

Roll out one sheet of puff pastry into an 11-inch square. Use a large pie plate to trace an 11-inch circle onto the dough. Place the circle onto the baking sheet. Repeat for the second sheet of pastry and refrigerate both.

Add almond frangipane filling onto the center of one pastry sheet. Leave a 1.5-inch margin at the edges. Insert the bean into the filling. Place the second pastry sheet on top and seal the edges. Brush egg wash on the top, score with a crisscross pattern, and prick slits to vent steam.

Bake for 15 minutes without opening the oven. Remove and dust with confectioners' sugar. Return to the oven and bake for 12–15 minutes more until golden brown.