Slice potatoes, zucchini, and eggplants into 1cm thick slices.
Heat olive oil in a large frying pan over medium heat.
Fry the vegetable slices in batches until golden and tender, then drain on paper towels and season with salt and pepper.
In a large saucepan, heat 2 tablespoons olive oil and sauté the chopped onion until soft.
Add minced garlic and cook for 1 minute.
Add beef mince and cook until browned.
Pour in red wine and let it reduce for 5 minutes.
Add crushed tomatoes, salt, white pepper, cinnamon, nutmeg, sugar, thyme, oregano, bay leaves, and chopped parsley.
Simmer the meat sauce uncovered for 45 minutes to develop flavor, stirring occasionally.
Preheat oven to 180°C (350°F).
To make bechamel sauce, melt butter in a saucepan over medium heat.
Whisk in flour and cook for 2 minutes to form a roux.
Gradually add milk while whisking constantly to avoid lumps.
Cook until sauce thickens and coats the back of a spoon.
Remove from heat and stir in nutmeg and half the shredded cheese.
Add egg yolks to the sauce and mix well.
Layer the bottom of a baking dish with fried potatoes.
Add a layer of fried zucchini, then a layer of fried eggplants.
Pour the meat sauce evenly over the vegetables.
Top with the bechamel sauce and sprinkle the remaining cheese on top.
Bake in the preheated oven for 45 minutes or until the top is golden and bubbling.
Let moussaka rest for 15 minutes before serving.
