Cook the split peas: Rinse the yellow split peas and simmer them in water until partially tender. Drain and set aside.
Cook the onion and meat: Heat oil in a heavy-bottomed pot. Add the onion and cook until soft and lightly golden. Add turmeric and black pepper, then add the beef or lamb and brown lightly.
Add tomato paste: Stir in the tomato paste and cook for 2–3 minutes until it darkens slightly and becomes fragrant.
Make the gheymeh: Add the partially cooked split peas and pierced dried Persian limes. Pour in the water or stock and bring to a gentle simmer.
Simmer: Cover and cook until the meat is tender and the split peas are fully cooked. Reduce any excess liquid so the gheymeh becomes thick and spoonable.
Bloom the saffron: Grind the saffron threads and combine them with a few tablespoons of hot water. Let it bloom for at least 10 minutes.
Prepare the rice: Rinse the basmati rice several times and soak it in salted water for 30 minutes to 2 hours. Drain, then parboil in generously salted boiling water for about 5-8 minutes. The grains should be tender outside but still firm in the center.
Layer the rice and gheymeh: Add oil to the bottom of a heavy pot and create a thin layer of rice for the tahdig. Add alternating layers of rice and gheymeh, finishing with rice. Make a few holes in the rice with the handle of a wooden spoon.
Steam: Drizzle the bloomed saffron over the rice. Wrap the lid with a clean kitchen towel, cover the pot, and steam over medium-high heat for several minutes. Reduce to low heat and cook for 40-50 minutes.
Rest and serve: Turn off the heat and let the Gheymeh Polo rest for 5-10 minutes. Gently fluff the rice, transfer it to a serving platter, and serve with the crispy tahdig.