Prepare the Eggplant: Sprinkle eggplant slices with salt and let sit for 30 minutes. Pat dry, brush with olive oil, and roast at 400°F (200°C) for 20-25 minutes, flipping halfway through. Set aside.
Prepare the Meat Sauce: Heat olive oil in a skillet, cook onion until softened, then add garlic. Brown the meat, add red wine, then stir in tomatoes, tomato paste, spices, salt, and pepper. Simmer for 20-25 minutes. Set aside.
Prepare the Béchamel Sauce: Melt butter, whisk in flour, then gradually add milk. Cook until thickened, stir in nutmeg and Parmesan. Cool slightly, then whisk in beaten eggs.
Assemble the Moussaka: Layer breadcrumbs, half of the eggplant, meat sauce, remaining eggplant, and béchamel in a baking dish. Top with Parmesan.
Bake: Bake at 350°F (175°C) for 45-50 minutes until golden brown. Cool for 15-20 minutes before serving. Garnish with parsley.