Place the puff pastry on a baking sheet and prick several times with a fork. Bake in the preheated oven at 200 ° C until light brown. Do the same with the second puff pastry.
For the filling:
cook a pudding with milk, vanilla pudding powder and sugar according to the instructions on the packet.
In the meantime, soak the gelatine in cold water.
Put the cooked pudding in a bowl and add the squeezed gelatin. Then stir the rum and the ground vanilla (alternatively also vanilla sugar or a little vanilla flavor) into the pudding. Stir the pudding cream in a cold water bath. Whip the cream until stiff. When the pudding cream starts to gel, fold in the whipped cream.
Place a square cake edge around a puff pastry base (you can also put it in a large casserole dish or cut something to size). Pour in the vanilla cream.
Cut the second puff pastry base lengthways once and then cut into 14 equal-sized rectangles. Place the puff pastry rectangles close together on the vanilla cream. Chill the cream slices for a few hours.
Remove the cake ring. Before serving, portion the slices and dust them with icing sugar.