Beat the softened butter and sugar together, then beat in the eggs. Stir in the almond powder. Add vanilla, rum and set it aside.
Roll out one sheet of puff pastry. Poke holes with fork.
Spread the almond filling over the center of the dough, leaving a 1 inch (1.2 cm) exposed border. If you wish, place a little porcelain figurine "fève" somewhere in the almond filling.
Brush the edges of the pastry with water and cover with another circle of dough on top and press down to seal the edges.
Use a paring knife to create a design on top of your galette, then brush with beaten yolk. Poke 3-5 holes in the top, to allow steam to escape while baking.
Place in the refrigerator for 1 hour.
Preheat oven to 380 degrees F. Bake for 30-35 minutes or until the pastry is golden brown. (Bake on the bottom rack of the oven).