Combine all the syrup ingredients in a saucepan. Bring to a boil, then remove from heat and let cool completely.

Beat the egg whites with 1/4 cup (50 grams) sugar until stiff peaks form to make a meringue.

Remove the meringue from the mixer and set aside in a bowl.

In the same mixer bowl (no need to wash), beat the yolks with another 1/4 cup (50 grams) sugar until pale and creamy.

Fold in 1/4 of the meringue into the yolk mixture to lighten it.

Remove the bowl from the mixer. Using a spatula, gently fold the remaining meringue into the yolk mixture with light, circular motions until fully combined. Set aside.

In a saucepan, combine the milk, heavy cream, and the remaining 1/2 cup (100 grams) sugar.

Heat over medium until it just starts to boil. Add the vanilla and semolina, then whisk constantly until the custard thickens. Stir well to prevent the semolina from sticking and burning.

Once the mixture is thick, remove from heat and add 2 tablespoons (30 grams) butter, stirring constantly. This makes the custard extra smooth.

Let the custard cool slightly, then gently fold in the meringue mixture with strong, confident strokes to fully combine. The semolina mixture is thicker, so mix well to ensure a uniform texture.

Butter your baking dish well, then start layering the phyllo sheets.

Place the first 4 sheets, arranging each so a corner covers one corner of the dish, letting the edges hang over evenly all around.

Add one more sheet in the center. Before adding each new sheet, generously brush with melted butter, letting it drip from the brush rather than spreading. This helps create airy, crisp layers.

Pour the custard over the phyllo, then top with another 4-5 sheets. Trim the excess phyllo around the edges if you prefer less crust, or fold it in if you like more, using the brush to help tuck it down.

Pour plenty of melted butter over the top and sprinkle lightly with water.

Bake in a preheated oven at 350°F (180°C) for 1 hour, until golden brown.

As soon as it comes out of the oven, pour the cold syrup over the hot pastry.