To cut down on any bitterness and to reduce the amount of oil the eggplant will need, place the eggplant in colander and season generously with the coarse salt.
Weigh down the eggplant and allow to sit for about 40 minutes (an easy way to do this is fill a 1-gallon plastic zip-lock bag with water, seal tightly and place over the eggplant).
Rinse the salt off the eggplant and pat dry.
Heat 1 tablespoon oil in a large sauté pan over medium-high heat, add eggplant and cook, stirring often, until golden brown on all sides, about 20 minutes. Remove from pan and set aside.
Heat remaining oil in the same pan and sauté the onion, garlic, lamb, cinnamon, allspice, salt and pepper until the lamb is cooked.
Stir in the crushed tomatoes. Lower the heat and simmer until sauce has slightly thickened, about 15-20 minutes. Add back the eggplant pieces. Taste and adjust seasonings to taste.
Place pasta in a large serving bowl and pour the sauce over the pasta. Garnish with the chopped fresh parsley and sprinkle lightly with the grated parmesan cheese – can serve more on the side.