Preheat your oven to 375 F (190 C).
Brush both sides of eggplant slices with olive oil and season with salt and pepper.
Roast the eggplant slices in the preheated oven for 15-20 minutes until tender and slightly browned. Set aside.
In a large skillet, cook the ground lamb or beef until browned. Remove excess fat.
Add chopped onions and minced garlic to the skillet. Saut until onions are soft.
Stir in diced tomatoes, ground cinnamon, ground allspice, salt, and pepper. Simmer for 15 minutes.
In a saucepan, melt butter over medium heat. Stir in flour to create a smooth paste.
Gradually whisk in milk, nutmeg, salt, and pepper. Cook until the sauce thickens.
Remove the sauce from heat and allow it to cool slightly. Slowly whisk in beaten eggs.
In a greased baking dish, layer roasted eggplant, meat sauce, another layer of eggplant, and top with b chamel sauce.
Bake at 375 F (190 C) for 45-50 minutes until the top is golden brown and the filling is set.
Allow the Moussaka to cool slightly before slicing and serving. Enjoy!