Chop the onions and cook them in a pot with a little oil until softened.
Add the lamb and lamb fat. Cook for a few minutes until the meat changes color.
Add the water, cover the pot, and cook over low heat until the lamb is completely tender.
Remove the cooked lamb and let it cool slightly. Grind the lamb together with the lamb fat.
Add turmeric, cinnamon, dried mint, black pepper, salt, and brewed saffron. Mix well.
If using lamb lung, cook it separately with onion, turmeric, salt, and black pepper until tender. Let it cool and grind it finely.
Place a portion of the meat mixture in a small greased frying pan and press it into a round, relatively thin patty.
Cook over medium-low heat until the bottom is lightly browned. Carefully turn and brown the other side.
Serve the hot Biryani over fresh Sangak bread with herbs, sliced onion, and optional nuts.