Pour milk into a large saucepan, and bring to a boil over medium heat. In a medium bowl, whisk together the semolina, cornstarch, 1 cup sugar and salt so there are no cornstarch clumps. When milk comes to a boil, gradually add the semolina mixture, stirring constantly with a wooden spoon. Cook, stirring constantly until the mixture thickens and comes to a full boil. Remove from heat, and set aside. Keep warm.
In a large bowl, beat eggs with an electric mixer at high speed. Add 1/2 cup of sugar, and whip until thick and pale, about 10 minutes. Stir in vanilla.
Fold the whipped eggs into the hot semolina mixture. Partially cover the pan, and set aside to cool.
Preheat the oven to 350 degrees F (175 degrees C).
Butter a 9×13 inch baking dish, and layer 7 sheets of phyllo into the pan, brushing each one with butter as you lay it in. Pour the custard into the pan over the phyllo, and cover with the remaining 5 sheets of phyllo, brushing each sheet with butter as you lay it down.
Bake for 40 to 45 minutes in the preheated oven, until the top crust is crisp and the custard filling has set. In a small saucepan, stir together the remaining cup of sugar and water. Bring to a boil. When the Galaktoboureko comes out of the oven, spoon the hot sugar syrup over the top, particularly the edges. Cool completely before cutting and serving. Store in the refrigerator.
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