Season the Lamb: Season the lamb pieces evenly with the kosher salt and ground black pepper.
Sear the Lamb: Heat 2 tablespoons of olive oil or ghee in a large Dutch oven or pot over medium heat. Add the lamb and sear for 5–6 minutes on each side, until the pieces are lightly golden brown.
Simmer the Lamb: Cover the lamb with water and add the cardamom pods, bay leaves, cinnamon stick, black peppercorns, and quartered onion. Bring the liquid to a boil, then reduce the heat to medium-low. Cover and cook for about 90 minutes, or until the lamb is tender.
Strain the Stock: Remove the cooked lamb and strain the broth, discarding the spices and onion. Reserve both the lamb and the stock. You will need 2 1/2 cups of stock for the rice and 2 cups for the jameed sauce. If necessary, add water to the stock until you have a total of 4 1/2 cups.
Toast the Rice: Heat 2 tablespoons of olive oil or ghee in a saucepan over medium heat. Add the turmeric, kosher salt, and white rice. Stir well and toast the rice for 1 minute.
Cook the Rice: Pour in 2 1/2 cups of the reserved lamb stock. Bring the mixture to a boil, then reduce the heat to low. Cover and cook for 20 minutes.
Rest the Rice: Remove the saucepan from the heat and let the rice stand, covered, for 5 minutes. Fluff gently with a fork and keep covered until ready to assemble.
Prepare the Jameed Sauce: In a large blender, blend the soaked jameed with 2 cups of lamb stock and the cornstarch until completely smooth. If using the substitute, blend the substitute ingredients together instead.
Thicken the Sauce: Pour the blended jameed mixture into the Dutch oven or pot used to cook the lamb. Cook over medium heat for 5 minutes, allowing the sauce to thicken. Add water if needed to maintain a soupy consistency. Do not allow the sauce to boil.
Warm the Lamb in the Sauce: Add the cooked lamb to the jameed sauce and cook over medium heat for 10 minutes. Keep the sauce below a boil.
Prepare the Bread Base: Arrange the torn markook or lavash pieces across a large serving platter. Ladle a few spoonfuls of the jameed sauce over the bread, allowing it to soak in.
Assemble the Mansaf: Spoon the cooked rice over the soaked bread, then arrange the lamb pieces on top.
Garnish and Serve: Finish with the toasted almonds and chopped parsley. Add the optional sliced green onions, radishes, or sumac red onions if desired. Serve the remaining jameed sauce in a separate bowl for spooning over each serving.