Preheat oven to 350 F.
In a bowl, combine semolina, cornstarch, 1 cup of the sugar and salt.
In the bowl of an electric mixer, beat eggs until light and fluffy, about 10 minutes. Add sugar and vanilla. Beat another 2 minutes, until thoroughly incorporated.
While the eggs are beating, heat milk but do not let it boil. As soon as the milk starts to steam, add semolina combination. Cook for 3-5 minutes, stirring constantly, until thickened.
Using a rubber spatula, slowly fold in the eggs a little at a time.
In a 9x13 casserole dish, layer 6-7 slices of phyllo, brushing melted butter in between each layer.
Pour the semolina pudding inside.
On top, again layer 6-7 sheets of phyllos, brushing melted butter in between each layer. Make sure to brush melted butter on the top layer.
With kitchen scissors, trim the edges of phyllo.
Bake for 30-40 minutes, until the top is golden brown.
Meanwhile, combine syrup ingredients in a saucepan and simmer on medium heat for about 10-15 minutes, until you have a thin syrup consistency.
Pour syrup on top of galaktoboureko after you remove it from the oven, making sure to pour the syrup over the edges and in the corners.
Chill in refrigerator for at least 2 hours, but preferably overnight.
Serve chilled.