In a heavy-bottomed, 3-quart saucepan, bring the milk gradually to a boil; do not allow it to scorch. Meanwhile, sift the semolina, cornstarch, 1 cup of the sugar, and salt together and gradually add to the boiling milk, stirring constantly with a wooden spoon. Cook slowly over medium heat until the mixture thickens and comes to a full boil, then remove from the heat.
Partially cover the pan and allow to cool. Butter a 9 x 12 x 3-inch baking pan and cover the bottom with 7 sheets of the filo, brushing butter generously between each and making sure that a few sheets come up the pan sides. Pour the custard into the pan over the filo. Cover with the 5 remaining sheets, brushing butter between each and on the surface. With the tip of a very sharp knife, score the top filo sheets into square or diamond shapes, being careful not to score as deeply as the custard. Bake on the center rack of a moderate (350 F) oven for 40 to 45 minutes, until crisp and golden chestnut in color and the custard is firm.