Make the custard. Begin by preparing the filling. Add the milk to a heavy bottomed saucepan and heat it just before boiling over medium heat. While the milk is heating, add the sugar, semolina, egg, and egg yolk to a large bowl and whisk until the ingredients combine. Once the milk has heated, remove from heat and pour 1 cup of hot milk into the egg mixture, whisking constantly to avoid cooking the eggs. Add the tempered egg mixture to the saucepan with the remaining warm milk, whisking constantly. Return the saucepan over medium-low heat and whisk until the mixture thickens and becomes smooth and creamy. This should take about 3-5 minutes. Remove the saucepan from heat and stir in the butter, vanilla, and Nutella until smooth.  

Preheat oven to 350 degrees F.  Line an 8x8-inch baking pan with parchment paper hanging over the edges.

Take one sheet of phyllo and gently place it into the bottom of the pan, allow it to hang over the edges of the pan. Use a pastry brush to sprinkle melted butter over the whole layer. Repeat the process with 4 more layers of phyllo (5 in total).

Evenly spoon the prepared custard filling over the phyllo layers and top with a layer of phyllo. Brush that layer with butter and repeat with 4 more sheets. Tuck the overhanging phyllo into the pan and sprinkle the brown sugar over the top layer.

Bake for 45-50 minutes, or until the top is golden brown and crispy.

Remove the bougatsa from the oven and allow it to cool for at least 15 minutes on a wire rack before removing from the pan. 

Use the parchment paper to lift the bougatsa from the pan and generously dust with powdered sugar. Cut into squares and serve warm.