Preheat the oven to 425ºF (220ºC).
Place the eggplant halves, skin side down, in a roasting pan large enough to accommodate them snugly. Brush the flesh with 4 tablespoons of olive oil and season with 1 teaspoon of salt and plenty of black pepper. Roast for about 20 minutes, until golden brown. Remove from the oven and allow to cool slightly.
While the eggplants are cooking, make the stuffing by heating the remaining 2 tablespoons olive oil in a large skillet. In a small bowl, combine the cumin, paprika, and ground cinnamon, and add half of this spice mix to the skillet along with the onions. Cook over medium-high heat for about 8 minutes, stirring often, before adding the lamb, walnuts, parsley, tomato paste, 1 teaspoon of sugar, 1 teaspoon salt, and some black pepper. Continue to cook and stir for another 8 minutes, until the meat is cooked.
Place the remaining spice mix in a bowl and add water, lemon juice, tamarind, the remaining 2 teaspoons sugar, the cinnamon sticks, and ½ teaspoon salt; mix well.
Reduce the oven temperature to 375ºF (195ºC). Pour the spice mix into the bottom of the eggplant roasting pan. Spoon the lamb mixture on top of each eggplant. Cover the pan tightly with aluminum foil, return to the oven, and roast for 1 ½ hours, by which point the eggplants should be completely soft and the sauce thick; twice during the roasting remove the foil and baste the eggplants with the sauce, adding some water if the sauce dried out. Serve warm, not hot, or at room temperature.