Begin by slicing the eggplants, zucchini, and potatoes into ¼-inch rounds. Sprinkle salt on the eggplant slices and set them aside to draw out moisture for about 30 minutes.

In a large skillet, heat olive oil. Add salted eggplant slices in batches until golden brown. Fry zucchini and potato slices until just tender. Drain on paper towels.

In a large pan, sauté chopped onion and minced garlic until translucent. Add ground meat, cooking until browned. Pour in red wine, reduce, then stir in crushed tomatoes and spices. Simmer until thickened.

In a saucepan, melt butter. Whisk in flour to create a roux, cook for 2 minutes. Gradually add milk, whisking continuously. Once thick, remove from heat and stir in egg yolks and cheese.

Preheat your oven to 350°F (175°C). In a deep baking dish, layer the sliced potatoes, fried eggplants, and zucchini. Spoon the meat sauce over, then pour béchamel sauce on top.

Bake for 40-45 minutes until golden brown and bubbly. Watch for a crust forming on top.

Let it rest for at least 30 minutes before slicing. This allows layers to set, making it easier to serve.