For the vegetables: Preheat the oven to 400 degrees F. Cook the potato slices for 5 minutes (do not cook longer) in heavily salted, boiling water. Meanwhile, slice the eggplant into 1/4-inch slices, brush with the olive oil and sprinkle with 1/2 teaspoons salt and the pepper on both sides. Place on a baking sheet and cook in the oven, 6 to 7 minutes per side. Set aside the potato and eggplant slices for assembly.
For the meat sauce: In a large saucepan, sweat the onions with some salt in the olive oil over medium heat. After 5 minutes, add the ground beef and cook until golden brown, 7 to 8 minutes. Add the oregano, cinnamon, nutmeg and garlic, and cook until fragrant. Turn the heat up to high, and then deglaze the pan with the red wine, allowing to bubble and reduce for 1 to 2 minutes. Add the tomato sauce and lower the heat to simmer for 5 minutes. Remove the sauce from the heat and set aside.
For the bechamel: In a large saucepan over medium heat, melt the butter and add the flour, whisking to make a paste. Whisk constantly for 2 minutes, allowing the mixture to bubble. Add the warm milk slowly, whisking constantly to avoid lumps. Once the sauce starts to come to a boil, reduce the heat to low and cook until thickened, about 10 minutes, whisking very frequently. Add the salt, pepper and nutmeg, and set aside.
For assembling the moussaka: Preheat the oven to 350 degrees F. Before assembling, taste each of the 4 layers and confirm that they are properly seasoned. Grease a 9-by-13-inch baking pan with vegetable oil. Lay out the potato slices, pressing gently into the pan. Sprinkle with 3 tablespoons of the Parmesan. Place the eggplant on top of the potatoes. Sprinkle with another 3 tablespoons of the Parmesan. Spoon the meat sauce on top, followed by 3 more tablespoons of Parmesan. Finish with pouring over the bechamel and top with the last 3 tablespoons of Parmesan. Cover with foil (sprayed lightly with vegetable oil) and bake for 30 minutes, then uncover and continue baking for an additional 30 minutes.