Prepare and Fry the Vegetables:
Slice the eggplants, zucchini, and potatoes into ¼-inch rounds. Lightly salt the eggplant slices and let them sit for about 30 minutes to draw out excess moisture and bitterness. Pat the eggplant dry.
Heat olive oil in a large skillet over medium-high heat. Fry the vegetable slices in batches until golden brown and tender. Transfer to a paper towel–lined plate to drain.

Sauté the Onion and Garlic:
In a large pot or skillet, heat olive oil over medium heat. Add the chopped onion and cook for 5 minutes until soft and translucent. Add the garlic and cook for another 1-2 minutes until fragrant.

Make the Meat Sauce:
Add the ground beef (or lamb) to the onion and garlic mixture. Cook, breaking it up with a spoon, until browned. Add the crushed tomatoes, cinnamon, nutmeg, white pepper, salt, sugar, oregano, thyme, and bay leaves. Stir and simmer for 10-15 minutes. Remove from heat and discard the bay leaves. Garnish with fresh parsley.

Prepare the Béchamel Sauce:
In a medium saucepan, melt the butter over medium heat. Stir in the flour to form a smooth paste. Gradually whisk in the milk, stirring constantly to avoid lumps. Cook until the sauce thickens into a creamy consistency. Add the egg yolks, nutmeg, and shredded cheese. Stir until the cheese is melted and fully incorporated.

Assemble the Moussaka:
Preheat your oven to 165°C (330°F fan-forced) or 175°C (350°F conventional).
In a large baking dish, layer the ingredients in this order:

• A base layer of potato slices, seasoned with salt and topped with a sprinkle of cheese.

• A layer of fried eggplant slices, also seasoned and sprinkled with cheese.

• A layer of zucchini, followed by a second layer of eggplant.

• Spread the meat sauce evenly over the vegetables.

• Pour the béchamel sauce on top, smoothing it into an even layer.

Bake and Rest:
Bake in the preheated oven for 40-45 minutes, or until the top is golden brown and bubbling. Check at the 30-minute mark to avoid overbrowning.
Let the moussaka rest for at least 30 minutes before slicing to allow the layers to set.