Halve the vanilla pod lengthwise and scrape out the pulp with the back of a knife. Bring milk, vanilla pulp and pod to the boil in a pot. Mix egg yolks and sugar until light creamy. Stir the starch into the sugar-egg mixture.
Add a part of the vanilla milk while stirring, then pour back to the remaining milk.
Bring the cream slowly to the boil while stirring. Pour cream into a bowl and cover the surface directly with foil. Chill the cream for about 45 minutes. Remove puff pastry from the fridge 5-10 minutes before use.
Unroll the puff pastry and place it on a baking tray with the baking paper. Cover the dough with another piece of baking paper and weigh down with a second baking tray so that the dough does not rise too much.
Bake in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for 25-30 minutes until golden brown.
Remove upper baking tray and dust dough with icing sugar. Caramelise under the hot oven grill. Cut the dough sheet in half lengthwise and crosswise into 30 rectangles of equal size (approx. 2.8 x 12 cm).
Stir the custard until smooth and fill into a piping bag with a medium-sized piping nozzle. Spread the cream in tuffs over 20 rectangles. Place 2 pastry plates with cream on top of each other and finish with a 3 plate (without pudding).
Serve immediately.