Slice the eggplants into 1/2-inch thick rounds and sprinkle generously with salt. Let sit for 30 minutes to draw out bitterness.

Rinse the slices under cold water, pat dry, and set aside.

Preheat the oven to 180°C (350°F). Toss the sliced potatoes and eggplant with olive oil, salt, and pepper. Spread in a single layer on a baking sheet and bake for about 20 minutes until slightly tender.

In a large skillet, heat olive oil over medium heat. Sauté chopped onions and minced garlic for 5 minutes until soft.

Add the ground meat, season with salt and pepper, and cook until browned, about 10 minutes. Deglaze with red wine, then add chopped tomatoes. Let simmer for 15-20 minutes.

In a saucepan, melt butter, then whisk in flour to form a roux. Gradually add milk, whisking continuously until thickened, about 5-7 minutes. Stir in cheese, nutmeg, and egg yolks off heat.

In a greased baking dish, layer baked potatoes, half roasted eggplant, meat sauce, remaining eggplants, and top with béchamel sauce.

Bake uncovered for about 60 minutes until top is golden brown and bubbly.