Bougatsa Cream

In a heavy-bottomed saucepan, combine the milk, semolina, sugar, vanilla, and salt.
Cook over medium heat, stirring constantly, until the mixture becomes a smooth cream.
Once it comes to a boil, remove from heat and add the butter, stirring until melted.
Transfer the cream to a wide bowl, cover with plastic wrap directly on the surface, and allow to cool and set.

Assembling the Bougatsa

Grease a rectangular baking pan thoroughly with a brush.
Layer 5 sheets of filo pastry in a crisscross pattern, making sure the edges hang over the sides of the pan.
Brush the sheets and overhanging edges generously with butter.
Pour the cooled cream over the filo pastry.
Fold the overhanging sheets inward and brush well with butter.
Layer the remaining 5 sheets on top of the cream, brushing butter between layers.
Tuck the overhanging top sheets into the pan edges and brush the surface with butter.

Baking

Preheat the oven to 180°C (356°F, fan-assisted).
Bake on the middle rack for about 35 minutes, until the filo pastry is puffed and golden brown.