Mix flour, powdered sugar, vanilla, and salt in a bowl.
Cut the butter into small cubes and crumble it into the flour until it has a sawdust-like consistency.
Quickly gather the dough with the egg and chill the dough for about half an hour.
Do not knead the dough too much.
TIP: It can advantageously be made in a food processor!
Roll out the shortcrust pastry on a floured surface to about 3-4 mm and cut out circles around 8-9 cm.
Mix all ingredients together into a uniform mass and let the marzipan cake mass rest in the refrigerator for about half an hour.
Take out the marzipan mass and form 16 small balls, each the size of a ping pong ball, around 23-25 grams, and place one ball on each shortcrust circle (use damp hands to ensure the marzipan mass doesn't stick).
Press and fold the shortcrust pastry in three places so it attaches to the marzipan mass.
Use three fingers and give it a light press so the shortcrust pastry sticks to the marzipan mass, forming its “triangle shape”.
Optionally, dip the hats in chopped pistachios.
Bake the hats in the oven at 200 degrees Celsius (392 degrees Fahrenheit) in a conventional oven for about 8-9 minutes until the tops and sides are golden.
Take them out and let them cool completely.
Melt the chocolate - temper it if you’d like - and dip the bottom of the Napoleon hats.
Scrape the bottom gently against the edge of the bowl so it becomes a thin and fine chocolate layer.
Place the hats upside down at a slant and let the chocolate set before serving!
Enjoy.