Preheat the oven to 400°F (200°C) and lightly grease a 12-cup muffin pan.
Heat the olive oil in a skillet over medium heat. Add the onion and cook for 3 to 4 minutes until softened.
Add the ground beef and cook until browned, breaking it into small crumbles as it cooks. Season with salt, then remove from the heat and set aside.
Roast the eggplant until completely tender. Let it cool slightly, remove the skin, and chop the flesh into small pieces.
In a medium saucepan, melt the butter over medium heat. Stir in the flour and cook for about 2 minutes while whisking.
Gradually pour in the milk, whisking constantly until the sauce becomes smooth and thick, about 5 to 7 minutes.
Stir in the nutmeg, season with salt, then fold the chopped roasted eggplant into the béchamel sauce.
Lightly flour a work surface and roll out the puff pastry. Cut it into twelve equal squares, about 5 inches each.
Press one pastry square into each muffin cup, allowing the corners to extend over the edges.
Spoon the cooked beef evenly into each pastry cup.
Top each with a generous spoonful of the eggplant béchamel mixture.
Sprinkle the mozzarella cheese evenly over the filling.
Brush the exposed pastry edges with the beaten egg yolk.
Bake for 10 to 15 minutes, or until the pastry is puffed and golden brown and the cheese is melted.
Allow the puff muffins to cool for a few minutes before carefully removing them from the pan. Serve warm.