Prepare the lamb and beans: Slice the onion thinly and sauté in a few tablespoons of oil until translucent. Add sliced garlic and sauté for another minute. Add the lamb pieces and sauté for 4-5 minutes until the meat changes color. Stir in turmeric, black pepper, and cumin powder. Add drained soaked white beans and sauté for a couple more minutes.
Simmer the lamb and beans: Add boiling water to just cover the meat and beans (about 4-4.5 cups). Add bay leaves, cinnamon sticks, and pierced dried limes if using. Bring to a boil, then cover and simmer gently for about 2 hours, stirring occasionally. Add salt halfway through cooking. Add some liquid saffron for color and flavor. If needed, add more boiling water to keep covered and continue cooking for another 30-45 minutes until lamb and beans are tender.
Prepare the rice: Bring water to boil in a pot. Add soaked and drained rice and cook for 8-9 minutes until about 80% cooked. Drain and rinse with cold water to remove excess starch and salt. Drain well and set aside.
Prepare the dill rice: Add 4-5 tablespoons of oil to the pot. Add some liquid saffron to the oil. Layer a small amount of plain rice at the bottom, then add a layer of chopped dill mixed with rice on top. Repeat layering until all rice and dill are used, finishing with dill on top. Make holes in the rice for steam to escape. Optionally add small pieces of butter on top.
Steam the rice: Place the pot on high heat for about 5 minutes until steam rises. Reduce heat to medium-low, cover the pot with a kitchen cloth and lid, and steam for 45-50 minutes until rice is fully cooked and crispy at the bottom (tadic).
Prepare the fried potatoes: Peel and dice potatoes to uniform size. Soak in cold water to prevent discoloration. When ready, heat enough oil in a pan and fry potatoes until golden and crispy. Drain excess oil and sprinkle with salt.
Serve: Serve the braised lamb and white beans alongside the dill rice and fried potatoes. Optionally accompany with fresh herbs (sapzi hordan) such as radish and green onion.