Slice the eggplants into ½-inch thick rounds and sprinkle them with salt. Let sit for 30 minutes, then rinse and pat dry. Preheat oven to 400°F (200°C), drizzle with olive oil, and roast for 20–25 minutes until tender.

In a skillet, heat olive oil over medium heat. Sauté the onion and garlic until translucent (about 5 minutes). Add ground beef and cook until browned. Stir in crushed tomatoes, tomato paste, cinnamon, oregano, and broth. Simmer for 20–25 minutes until thickened.

Melt butter in a saucepan over low heat. Whisk in flour and cook for 1-2 minutes. Gradually add warm milk, whisking to avoid lumps. Thicken for about 5-7 minutes, then remove from heat and stir in the beaten egg and grated cheese, seasoning with nutmeg.

In a greased baking dish, layer half of the roasted eggplant, then half of the meat sauce. Add remaining eggplant, then the rest of the meat sauce. Pour béchamel over the top and smooth out.

Bake at 350°F (180°C) for 45 minutes until golden and bubbling. Let it rest for 10-15 minutes to set before slicing.