Preheat your oven to 400°F (200°C). Slice the eggplants into rounds, brush with olive oil, and season with salt and pepper. Roast for about 20 minutes until soft and golden.

In a skillet, sauté chopped onion and minced garlic in olive oil until translucent. Add ground beef and cook until browned, then stir in crushed tomatoes, tomato paste, beef broth, cinnamon, oregano, salt, and pepper. Simmer for 10-15 minutes.

In a saucepan, melt the butter, add flour and whisk for 2 minutes. Gradually whisk in milk until thickened. Remove from heat and mix in an egg, grated cheese, salt, pepper, and nutmeg.

In a baking dish, layer half the roasted eggplant, then pour the meat sauce on top, followed by the remaining eggplant, and finish with béchamel sauce.

Bake in the oven at 350°F (180°C) for 40-45 minutes until top is golden. Rest for 15 minutes before slicing.