Heat 1 tablespoon of olive oil in a large Dutch oven over medium-high heat. Add the lamb cubes and brown them on all sides, about 6 minutes. Remove the lamb and set it aside.
Add the remaining tablespoon of olive oil to the pot. Cook the onions until they soften, about 5 minutes. Stir in the garlic, turmeric, and cinnamon and cook for 1 minute more.
Return the lamb to the pot. Add the tomato paste and stir to coat the meat. Pour in the beef broth and bring the mixture to a simmer. Cover and cook for 45 minutes.
While the stew simmers, heat a skillet over medium heat. Add the eggplant cubes and cook, stirring occasionally, until they start to soften and brown lightly, about 8 minutes.
Add the eggplant to the stew. Stir in the pomegranate molasses, salt, and pepper. Simmer uncovered for 20 minutes until the lamb is tender and the sauce thickens slightly.
Sprinkle with chopped parsley before serving.