For the eggplant: Layer the eggplant slices in a colander or arrange them in a single layer on as many baking sheets as needed. Salt each piece well and let sit for about 1 hour. Rinse with cold water and pat dry.
Line a baking sheet with paper towels. Heat the olive oil in a large saute pan over medium-high heat. Fry the eggplant briefly in batches, 1 1/2 to 2 minutes per side. Set aside to drain on the paper towels.
For the meat sauce: Heat the olive oil in a large, heavy skillet over medium-high heat. Add the onions and cook until translucent, 7 to 8 minutes. Add the ground beef and cook until lightly browned. Add the tomatoes, allspice, cloves, garlic, bay leaves, cinnamon, salt, pepper and a little water if needed. Cook for about 5 minutes. Stir in the wine and tomato paste and simmer until all of the liquid has been absorbed. Remove from the heat and cool slightly.
Make the bechamel: Heat the butter in a large saucepot over medium heat. Add the flour and cook, stirring with a wooden spoon or whisk, until lightly colored, 5 to 6 minutes. Add the milk and cook, whisking constantly, until thickened, 5 to 6 more minutes.
Remove from the heat. Whisking vigorously, add the beaten eggs (whisking constantly will prevent them from curdling). Stir in the cheeses. Add the nutmeg and season with salt and pepper.
Preheat the oven to 350 degrees F.
Lightly oil a large (9 by 13-inch) baking dish. Sprinkle the breadcrumbs evenly in the bottom of the dish. Place a layer of eggplant slices over the breadcrumbs. Spread the meat sauce evenly over the eggplant and cover with another layer of eggplant. Gently pour the bechamel over the top and sprinkle with the grated cheese. Bake until the bechamel is thick and golden brown on top, 45 minutes to 1 hour. Serve warm.
This recipe was provided by a professional chef or restaurant and makes a large quantity. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.