For the custard: In a saucepan, add the milk, cocoa powder, butter, sugar, split vanilla bean, and salt. Heat over medium heat. Gradually add the semolina while stirring for a few minutes until the mixture thickens. Remove from the heat, add the dark chocolate, and stir until it melts.

Set the mixture aside for a few minutes to cool to a warm temperature. In a bowl, whisk the eggs and add them quickly to the custard, stirring with a whisk. Transfer the custard to a bowl. Cover it with plastic wrap so that it touches the surface of the custard to prevent it from forming a skin. Let it cool.

Preheat the oven to 200°C with fan mode. Bake on the middle rack.

For assembling the bougatsa: Lay out 4 sheets of puff pastry, buttering between each layer. Spread the cooled chocolate custard on the sheets, leaving a 2cm border around the edges. Place pieces of milk chocolate inside the custard. Roll the pastry into a log. Repeat the process with the remaining sheets, buttering each layer. Bake at 180°C for about 30 minutes.

Once baked, cut the chocolate bougatsa with a sharp knife, drizzle with melted chocolate, and sprinkle with powdered sugar.