1. Preheat the grill to medium-high heat.
2. Brush the eggplant slices with olive oil and grill until tender and slightly charred, about 3-4 minutes per side. Set aside.
3. In a large skillet, cook the ground beef over medium heat until browned. Add the chopped onion and minced garlic, and cook until softened.
4. Stir in the canned tomatoes, oregano, cinnamon, salt, and pepper. Simmer for 15-20 minutes until the sauce thickens.
5. Preheat the oven to 180°C (350°F).
6. To make the béchamel sauce, melt the butter in a saucepan over medium heat. Stir in the flour and cook for 1-2 minutes. Gradually whisk in the warm milk until smooth and thickened. Add the grated nutmeg and season with salt and pepper. Remove from heat and stir in the beaten egg yolk.
7. In a baking dish, layer half of the grilled eggplant slices, followed by the meat sauce, and then the remaining eggplant slices. Pour the béchamel sauce over the top, spreading it evenly.
8. Bake in the preheated oven for 30-40 minutes, until the top is golden and bubbly. Let it cool for a few minutes before serving.