For the cream filling, cut the vanilla pod lengthwise and scrape out the pulp.
Put milk, salt, 100 g sugar, vanilla pod and vanilla pulp in a pot. Bring to the boil and pour in the semolina while stirring. Simmer over low heat for about 5 minutes while stirring. Remove from the heat and let cool down briefly.
Whisk the eggs in a bowl. Stir 3-4 tablespoons of semolina porridge into the eggs. Then stir in the remaining semolina. Place foil directly on the semolina, chill for about 1 hour.
Melt the butter in a small pot. Grease a tart or springform pan (26 cm Ø). Spread out the dough sheets one by one, cut them into approx. 9 pieces each. Brush each sheet with the butter. Place half of the dough pieces in the mould, slightly overlapping, so that several layers (approx. 5, each layer consisting of several sheets) are created. Add semolina mixture and smooth it down. Lay the rest of the dough back on top, overlapping again.
Bake in the preheated oven (electric range: 175 °C/ convection oven: 150 °C/ gas: level 2) on the lower rack for approx. 45 minutes. Heat 100 g sugar, 125 ml water, lemon juice, zest and cinnamon stick in a pot, bring to the boil and simmer for approx. 10 minutes. Remove lemon zest and cinnamon stick. Take the pâté out of the oven, place it on a baking tray. Pour hot syrup evenly over the pâté and let it cool down. Cut into pieces and dust with icing sugar.
Note. Semolina cream becomes sliceable during baking