Boil the milk with the sugar and the semolina and mix constantly with the whisk until the cream is firm. Add the vanilla extract, stir gently and remove from the heat. Add the egg continuing to stir until it is incorporated into the cream. Butter 5 pastry sheets and put them on top of each other.
Take another pastry sheet, butter it and fold it in four.
Place it in the middle of the pastry sheet you have already spread and add the cream on top of it. Fold the outer pastry sheets, covering the cream and forming a square.
Put the bougatsa on a backing pan with non-stick paper underneath it. Butter the surface and bake in a preheated oven at 180° C for about half an hour until our bougatsa gets a golden color.
Once it is cool, sprinkle with powdered sugar and cinnamon.