Prepare Eggplant:
Sprinkle eggplant slices with salt and let sit for 20–30 minutes to draw out moisture. Rinse and pat dry. Brush with olive oil and roast at 400°F (200°C) for 20 minutes until lightly browned.
Make Meat Sauce:
In a skillet, heat 1 tbsp olive oil over medium heat. Sauté onion until translucent, then add garlic and cook 1 minute. Add ground meat and cook until browned. Stir in crushed tomatoes, tomato paste, wine, cinnamon, allspice, nutmeg, salt, and pepper. Simmer 15–20 minutes until thickened. Stir in parsley and set aside.
Prepare Béchamel Sauce:
In a saucepan, melt butter over medium heat. Stir in flour and cook 1–2 minutes. Gradually whisk in warm milk and cook until thickened. Remove from heat, season with nutmeg, salt, and pepper. Slowly whisk in eggs, then add Parmesan cheese.
Assemble Moussaka:
In a greased 9x13-inch baking dish, layer half of the eggplant slices. Spread half of the meat sauce over the eggplant. Repeat layers, finishing with eggplant on the bottom and topping with béchamel sauce.
Bake:
Bake at 350°F (175°C) for 45–50 minutes, until the top is golden brown and bubbling. Let rest 15–20 minutes before slicing.