Heat the oil in a heavy-based saucepan, preferably cast-iron, and toss the quartered onion in the oil for a couple of minutes, until lightly golden. Add the lamb shanks and turn to seal on all sides. The meat should not be browned at this stage.
Add the turmeric and stir to coat the shanks evenly. Drain the split peas and add to the pan, then add the dried limes.
Pour the boiling water into the pan and stir well. Bring back to the boil, then reduce the heat and cover the pan with a lid. Simmer gently for approximately 1½ hours until the shanks are nearly cooked (you should be able to separate the meat from the bone with a fork) and the split peas are al dente. Keep the heat low and keep the lid on the pan to retain as much of the liquid as possible.
Drain and add the potatoes and the tomato purée/tomato paste to the pan and stir to mix. Leave to simmer very gently until the potatoes are cooked, approximately 30 minutes. Season to taste.
Add the red kidney beans and simmer for a further 10–15 minutes. Add the lemon juice and simmer for another 5 minutes. Just before serving, add the liquid saffron and mix well.
Serve with warm flat bread such as pitta or lavash (very thin Persian bread) with a side dish of yogurt and fresh herbs.