Cut out 2 circles from the puff pastry with the lower part of a cake form. Bake them 1 at a time in a preheated 392°F (200 °C), without poking holes in them.
After baking them, leave them to cool. They will have increased in size during baking. Divide each layer into 2 parts. Bake the cuttings as well.
Prepare the cream: Put the milk to boil, while gradually adding sugar to taste. Separate the egg yolks from the egg whites. To the yolks, add the starch, diluted with a little water.
To the boiling sweetened milk, add the egg yolks in a thin trickle while stirring constantly, then add the butter, vanilla and rum.
Leave to boil a bit. In the meantime, beat the egg whites to snow, while adding a little sugar to taste. Add them carefully to the cream. Leave 2-3 min. to boil while stirring nonstop.
Alternate between cake layer and cream in the cake form, finishing off with cream. Remove the sides of the form and smear the sides with cream. Crumble the baked cuttings and stick them all over the cake. Decorate with caramel.