Set aside 1 cup of milk and pour the rest into a saucepan with most of the sugar. Heat over high heat until warm.

In a bowl, lightly beat the eggs with the reserved milk, remaining sugar, and semolina. Mix well.

When the milk is hot but not boiling, add the egg mixture to the saucepan. Whisk constantly until the custard thickens.

Once thickened, remove from heat (it doesn't need to be very thick, as it will bake in the oven). Stir in the vanilla and butter until melted. Cover the custard with plastic wrap and let it cool completely.

Butter a 16-inch (40 cm) round or rectangular baking pan (or a smaller one for a thicker custard). Layer half the phyllo sheets in the pan, brushing each sheet generously with butter and arranging them in a crisscross pattern.

Pour the cooled custard over the phyllo. Fold the overhanging phyllo edges inward, brushing with butter. Cover the custard with the remaining phyllo sheets, buttering each one well.

Bake in a preheated oven at 350°F (180°C) for about 1 hour, depending on your oven and pan size.

Tuck any overhanging phyllo around the edges of the pan using a spatula. Score the top lightly into pieces, pour any leftover butter over the top, and sprinkle the surface lightly with a little water.

When the dessert comes out of the oven, spoon the hot syrup over it, a little at a time, and let it cool completely.

To make the syrup: In a saucepan, combine the water, sugar, cinnamon stick, and lemon peel. Boil for just 5 minutes without stirring. Add the juice of half a lemon and let it cool slightly.

Cut into pieces and serve.