Line a baking pan with parchment paper and place one sheet of puff pastry on the bottom.

In a saucepan over medium heat, add the milk, sugar, butter, and vanilla. Stir until the milk is hot and the sugar has dissolved. Then add the semolina and keep stirring constantly until the mixture thickens into a cream. Remove from heat and continue stirring for a little longer.

Pour the cream over the puff pastry in the pan. Fold the edges of the bottom pastry inward, then place the second sheet of puff pastry on top, tucking the edges underneath. Use a knife to poke small holes in the surface. Bake at 350°F (180°C) for about 40-45 minutes, or until the pastry is golden brown.