For the pastry cream: Cut the vanilla bean lengthwise and scrape out the seeds. Rub it together with the vanilla powder into the sugar until the specks are nicely distributed and you no longer see lumps.
Add the egg yolks and whip until a white, frothy mass, preferably in a food processor.
Warm the milk in a separate saucepan. Pour a splash of warm milk into the sugar mixture. Mix well. Gradually add the rest of the milk.
Place the mixture on the heat and slowly bring to a boil while stirring vigorously with a whisk. Remove the pot from the heat when the mixture starts to bubble and 'pop'. It should be quite thick and smooth. If it's still too runny, cook a little longer.
Pour the mixture through a sieve to remove any remaining cooked egg or eggshell.
Immediately cover the cream with cling film and seal well at the edges to avoid a dirty skin forming. Let cool to room temperature.
For the frangipane: Cream the butter until soft and add the egg and rum. Mix the powdered sugar, cornstarch, and almond powder and gradually add it to the butter while stirring.
Combine the frangipane with the pastry cream and let rest overnight in the refrigerator.
The next day – For finishing: Preheat the oven to 185 °C.
Place a sheet of baking paper on the baking tray and arrange the first sheet of puff pastry on it. Brush the edges with a mixture of beaten egg yolk and milk ('glazing').
Pipe (with a piping bag) or spread the rich frangipane filling onto the puff pastry base, but stay at least 2 cm away from the edge. Place the bean on it. Place the second half of the puff pastry on top and press the edges tightly together.
Decorate the edge with 'waves': press with your index and middle finger into the edge of the dough and push back about 2 cm with the handle of a spoon between your two fingers. Go all the way around like this.
Glaze the edge with egg yolk and milk, and make a few arcs on the top with a sharp knife, from the center to the edge. Bake for 25 minutes in the oven, let cool and serve at room temperature.
