Place the egg yolks in a bowl and whisk until combined.

Split the vanilla bean and scrape out the seeds. Add both the seeds and the vanilla bean to a heavy-bottomed saucepan.

Add the milk, semolina, sugar, and cornstarch. Whisk everything together.

Bring the mixture to a gentle boil, then reduce the heat and cook while stirring until it begins to thicken.

Gradually add a little of the hot milk mixture to the egg yolks while whisking continuously. Continue until the yolks have warmed up, then pour the egg mixture back into the saucepan.

Cook over low heat, stirring constantly, until you have a thick, creamy custard.

Remove from the heat and let the custard cool completely.

Preheat the oven to 350°F (175°C).

Lightly grease a roughly 8 x 12-inch baking dish with some of the melted butter.

Place the phyllo sheets in the baking dish one at a time, brushing each layer lightly with melted butter before adding the next sheet.

Spoon the cooled custard into the center. Fold the overhanging phyllo loosely over the filling. It doesn’t need to look perfect; slightly crumpled phyllo actually works really well here. If you like, you can crumple an extra sheet of phyllo over the top.

Use a sharp knife to make a few small cuts in the top.

Brush the top lightly with the remaining melted butter.

Bake for about 30 minutes, or until the phyllo is golden brown and crisp.

Let the bougatsa cool slightly, dust generously with powdered sugar, and cut into pieces before serving.