Spread your puff pastry to a height of about 2 mm, and form 2 circles of about 23 cm in diameter (you can use a tart ring to get identical sizes). Reserve in the refrigerator.
Mix the creamy butter with a fork. Add the egg and the rum, mix well.
Stir in flour, sugar and almond powder. Mix until you obtain a homogeneous paste.
Place the first dough on a baking sheet covered with parchment paper. Spread the filling evenly over the surface of the dough, leaving a border of about 2 cm.
Place the trinket in the stuffing, at the edge of the border (to be less likely to cut into it).
Moisten the edge of the dough with a little water, then place the 2nd circle on top. Seal the 2 doughs well by pressing with your fingers on the edge (or you can use a 20 cm ring, place it on the dough, around the stuffing and press).
Put the galette in the refrigerator for 30 minutes.
Preheat the oven to 180°C (350°F).
Take out the galette. Brush it with the egg yolk mixed with the milk. Make a small hole in the center (to allow humidity to evaporate off during cooking). Using a sharp knife, make the decoration of your choice on the top of the galette (though be careful not to cut the dough, just do some notches).
Cook for about 40 minutes.