Heat a large pot over medium heat. Add the lamb pieces and cook until browned on all sides, about 8 minutes. Remove the lamb and set it aside.
In the same pot, add the diced onion and cook until softened, about 5 minutes. Stir in the minced garlic and cook for 1 minute more.
Return the lamb to the pot. Add the turmeric, cinnamon, salt, and pepper. Stir to coat the meat with the spices.
Pour in the broth and pomegranate molasses. Bring the mixture to a simmer. Add the rinsed barley, cover the pot, and cook for 45 minutes, stirring occasionally.
After 45 minutes, check the barley for tenderness. If needed, cook 10 minutes longer until the barley is soft and the lamb is fork-tender.
Turn off the heat. Stir in the chopped walnuts. Ladle the stew into bowls and top each serving with pomegranate seeds and fresh parsley.