In a bowl, dissolve 2 tsp of salt in 1 quart of water. Add the eggplant, cover with a plate to keep the slices under the water, soak for 30 minute.
Meanwhile, in a large dutch oven or cast-iron casserole pot, heat 2 Tbl of the oil. Season the lamb with salt and pepper and cook over high heat, turning once until well browned, about 5 minutes per side. Add the onion and cook over moderate heat, stirring, until softened about 10 minutes. Add 3 quarts of water, the pomegranate molasses, split peas, dried chiles, baharat and coriander and bring to a boil. Reduce the heat to low and simmer for 45 minutes stirring and skimming every so often.
Drain the eggplant and pat dry. In a large non-stick skillet, heat 1 1/2 Tbl of the oil. Add 1/3 of the eggplant and cook over med-high heat until browned, 3 minutes per side; transfer to paper towels to drain. Brown the remaining eggplant in the 3 Tbl of oil. Add the eggplant to the lamb and simmer over low heat, stirring until the lamb is tender, 45 minutes.
Transfer the lamb to a rimmed baking sheet, remove the meat from the bones and cut into 1-inch chunks. Boil the stew over high heat, skimming, until the liquid has reduced to 3 cups, about 40 minutes.
Return the lamb to the stew and season with salt and pepper. Divid the pita among 4 bowls, ladle the soup on top and serve.