Preheat oven to 400 degrees F.

Cook potato slices in boiling, salted water for 5 minutes.

Slice eggplant into 1/4-inch slices, brush with olive oil, and season with salt and pepper.

Bake eggplant slices for 6-7 minutes per side.

Set aside potato and eggplant slices.

In a large saucepan, sauté chopped onions with salt in olive oil over medium heat for 5 minutes.

Add ground beef and cook until golden brown, about 7-8 minutes.

Add oregano, cinnamon, nutmeg, and garlic; cook until fragrant.

Deglaze the pan with red wine, allowing it to bubble and reduce for 1-2 minutes.

Add tomato sauce and simmer for 5 minutes.

Remove meat sauce from heat.

For the béchamel, melt butter in a saucepan over medium heat.

Add flour and whisk to make a paste. Cook for 2 minutes, whisking constantly.

Slowly add warm milk, whisking constantly to avoid lumps.

Bring the sauce to a boil, then reduce heat to low and cook until thickened, about 10 minutes, whisking frequently.

Add salt, pepper, and nutmeg to the béchamel.

Preheat oven to 350 degrees F.

Grease a 9x13-inch baking pan with vegetable oil.

Lay out potato slices in the pan and sprinkle with 3 tablespoons of Parmesan.

Place eggplant slices on top of the potatoes and sprinkle with 3 tablespoons of Parmesan.

Spoon meat sauce on top and sprinkle with 3 tablespoons of Parmesan.

Pour béchamel sauce over the meat sauce and top with the remaining 3 tablespoons of Parmesan.

Cover with foil (sprayed lightly with vegetable oil) and bake for 30 minutes.

Uncover and bake for an additional 30 minutes.