For Frangipane dough:
Mix the butter with the sugar until creamy. Add the egg, vanilla, and almond flour, mixing until well combined.
Roll out the puff pastry into a 35x28 cm rectangle, place it on baking paper, and spread the frangipane dough over it, leaving a 5 cm border all around. Arrange the sliced apples, slightly overlapping them. Fold the edges of the crust over the filling, sealing them, brush the edges with beaten egg, sprinkle with brown sugar if desired, and bake the galette for 30-40 minutes at 190°C or until golden.
Let the galette cool completely.
Enjoy with pleasure!