Heat the olive oil in a large pot over medium heat. Add the lamb neck pieces and brown them on all sides for about 8 minutes. Remove the lamb and set it aside.
Add the sliced onions to the same pot and cook until softened and lightly golden, about 6 minutes. Stir in the garlic, turmeric, and cinnamon and cook for 1 minute more.
Return the lamb to the pot. Pour in the broth and bring the mixture to a simmer. Cover and cook on low heat for 1 hour and 30 minutes, until the lamb is tender.
Stir the ground walnuts and pomegranate molasses into the pot. Continue simmering uncovered for 20 minutes so the broth thickens and the flavors blend.
While the stew simmers, cook the bulgur in a separate saucepan according to package directions using 2 cups of water. Season with salt and pepper.
Taste the stew and adjust salt and pepper as needed. Serve the stew over the cooked bulgur and top each bowl with pomegranate seeds and chopped parsley.