For the semolina cream cake, stir the semolina, cornstarch and vanilla sugar well with the milk (preferably with a whisk). Bring to a boil over medium heat, stirring constantly with a whisk or wooden spoon so that the cream does not burn at the bottom of the pot.
The cream should not be very runny or very stiff. When it is ready, add 1 tablespoon of butter, stir well and remove from heat. Let cool.
Butter a baking dish about 24×29 cm and place one by one 3 of the strudel dough sheets nicely. Using a brush, brush the pastry sheets with melted butter. CAUTION. The dough sheets should hang around the form and not cut.
Add the eggs to the semolina cream and mix well again until a homogeneous mass is formed. Spread the cream in the baking dish. Carefully “close” the sheets that hang around the outside (at the same time brush with a little butter) until the cream is well covered.
Meanwhile, spread the last sheet of dough on 2 folds with butter and cover the cake. Make some holes with a knife and bake in the oven at 180 °C on the lowest rack for about 30 minutes.
For the syrup, boil sugar with water and the cinnamon stick until the sugar is dissolved (about 5-10 minutes). Let the syrup cool down.
Remove the cake from the oven and carefully pour the syrup over it with a tablespoon. Let rest for about 2 hours so that the syrup is absorbed by the cake.