Preheat the oven to 400°F (200°C). Lay the eggplant slices on a baking sheet, drizzle with olive oil, season with salt and pepper, and roast for 20-25 minutes, flipping halfway through.
- In a large skillet, heat 1 tablespoon of olive oil over medium heat. Add the onion and garlic, cooking for 3-4 minutes. Add the ground lamb or beef, cooking until browned and cooked through.
- Add the crushed tomatoes, red wine (if using), oregano, cinnamon, salt, and pepper. Simmer for 15-20 minutes until the sauce thickens. Set aside.
- In a saucepan, melt butter over medium heat for the béchamel sauce. Stir in flour and cook for 1-2 minutes. Gradually whisk in milk and cook until thickened. Remove from heat, then stir in nutmeg and 1/2 cup Parmesan. Let the sauce cool slightly before whisking in eggs.
- Preheat the oven to 350°F (175°C). In a greased baking dish, layer the eggplant slices, then half of the meat sauce, followed by another layer of eggplant and the remaining meat sauce.
- Pour the béchamel sauce over the top and sprinkle with the remaining 1/2 cup of Parmesan.
- Bake for 45-50 minutes until golden brown and bubbling. Let the moussaka rest for 10 minutes before serving.