Cut the eggplants crosswise into 1/2 inch thcik slices. Sprinkle with 1 1/2 teaspoons of the salt and stack in a colander. Place a plate on top, weight it down and drain for 20 minutes. Pat the slices dry with paper towels and set aside.
Preheat the oven to 425 F. Brush a nonstick baking sheet and both sides of the eggplant slices with 3 tablespoons of the olive oil. Place the slices in a single layer on the baking sheet and cook for 25 minutes, until lightly browned. Set aside.
Heat 2 tablespoons of the remaining olive oil in a large saute pan set on high heat until sizzling, about 2 minutes. Add the potatoes, sprinkle with 1/4 teaspoon of the salt and 1/2 teaspoon of the pepper and cook until they begin to brown, about 5 minutes. Transfer the potatoes to a 9 x 13 inch baking dish, spreading them evenly. Set aside.
Heat the remaining olive oil in the same pan set on high heat. Add the ground lamb or beef and cook the onion, garlic, bay leaves, cinnamon, allspice, nutmeg, thyme and the remaining salt and pepper and cook for 3 minutes. Return the browned meat to the pan and cook for 1 minute. Stir in the wine and cook until reduced by half, about 1-2 minutes. Add the tomato sauce and beef stock and bring to a boil. Reduce the heat to medium and simmer for 10 minutes, until the sauce has thickened.
Preheat the oven to 375 F. To assemble the dish, arrange half the reserved eggplant slices over the potatoes in the baking dish. Top with the meat sauce and then with the remaing eggplant slices. Pour the bechamel sauce over the top and sprinkle with the grated Parmigiano Reggiano cheese. Bake for 45 minutes, until the top is golden brown. Remove from the oven and cool for 10-15 minutes. Cuts into 8 squares and serve.
This is a great dish to assemble and bake a day ahead. The flavors will be better the next day and it will cut more easily. Individual pieces can be reheated in the microwave or the whole dish can be reheated, uncovered, in a 350 F oven for 1 hour.
Wine Suggestion - Gewurztraminer