Roll out the puff pastries to a height of around 2mm. Preferably, take them to the refrigerator for 30 minutes.
Smash the soft butter with a fork. Add the egg and the rum, mix it.
Add the flour, the sugar, the pinch of salt and the almond powder. Mix until you get a homogeneous cream.
Slightly roll out again the first part of the pastry. Then, shape a circle around 23cm in diameter (you can use a pie ring mold to aid you). Place the pastry on a baking sheet covered with parchment paper.
Spread the almond cream in a uniform manner over the pastry, leaving a free room around 2 cm on the edges.
Spread the orange compote over the almond cream.
Place the bean in the filling, close to the edge (to get less risk of cutting it).
Slightly roll out again the second part of the pastry. Then, place it over the King Cake. Confine the filling with the pastry, pressing firmly all around the edges.
Moisten the pastry bottom edge with a small amount of water, then, seal both pastry sides together by firmly pressing with your fingertips.
Take the King Cake to the refrigerator for 30 minutes at least.