Slice eggplants about 1/2 inch thick, sprinkle with salt and let sit 20 minutes to draw out moisture; pat dry.
Brush eggplant slices with olive oil and roast or pan-fry until golden; set aside.
In a large skillet, heat oil and sauté chopped onion until translucent, then add minced garlic and cook 1 minute.
Add ground beef or lamb and brown thoroughly, breaking up pieces as it cooks.
Stir in tomato paste, crushed tomatoes, red wine (if using), cinnamon, oregano and bay leaf; simmer 20–30 minutes until thickened.
Season the ragu with salt, pepper and stir in chopped parsley; remove bay leaf.
Preheat oven to 180°C (350°F). Prepare béchamel by melting butter, whisking in flour to form a roux and cooking 1–2 minutes.
Gradually whisk warmed milk into the roux until smooth and simmer until thickened; remove from heat and temper in egg yolks, then add cheese, nutmeg, salt and pepper.
Layer half the eggplant in a baking dish, spread the meat ragu over it, top with remaining eggplant and pour béchamel evenly over the top.
Bake 35–40 minutes until béchamel is set and golden; let rest 15–20 minutes before slicing and serving.