1.Preheat the oven and prepare the vegetables: Thinly slice the eggplants, potatoes, and zucchini if using.
2.Fry the sliced vegetables in olive oil until golden brown, then drain on paper towels.
3.In a pan, cook the ground beef or lamb with chopped onion and minced garlic until browned.
4.Add grated tomatoes, tomato paste, spices, thyme, bay leaf, salt, oil, and parsley. Simmer for 20 minutes.
5.In a separate pan, make the Mornay sauce by whisking olive oil and flour over medium heat, then gradually adding warm milk until thickened.
6.Stir in nutmeg, black pepper, and egg yolks. Remove from heat and add grated cheese.
7.Layer the fried vegetables, meat mixture, and Mornay sauce in a baking dish, repeating until all ingredients are used.
8.Top with remaining Mornay sauce and cheese, then bake in the oven until golden and bubbly, about 45 minutes.
9.Let the Moussaka cool for a few minutes before serving at room temperature.