Put the butter, sugar, eggs, rum, flour and the ground almonds in a bowl and mix with the mixer to a relatively smooth mass.
Grease a porcelain baking dish and line it with a layer of puff pastry. Spread the almond mixture on top and put the second layer of puff pastry on top and brush with egg yolk.
Press the edges of the two layers of puff pastry together so that the galette is closed on the side. Then bake for 35 - 40 minutes in a preheated oven at 180 ° C top / bottom heat.