In a large mixing bowl, combine the lamb shoulder, whisked yogurt, ginger-garlic paste, Kashmiri red chili powder, turmeric powder, garam masala, salt, and lemon juice. Mix thoroughly to coat all the meat pieces. Cover and refrigerate to marinate for at least 1 hour.

Heat the cooking oil in your heavy-bottomed pot over medium heat. Add the thinly sliced onions. Fry them, stirring frequently to ensure even browning, for 12 to 15 minutes until they turn a deep golden brown and crisp up. Using a slotted spoon, remove half of the fried onions and spread them on a plate lined with paper towels to drain; leave the remaining onions and oil in the pot.

Place the pot with the remaining fried onions and oil back over medium-high heat. Add the slit green chilies and the marinated lamb (along with all marinade). Sear the meat, stirring continuously, for 5 to 7 minutes until the lamb changes color from pink to a dull brown. Pour in 240 ml of water and bring to a simmer. Cover with a tight lid, reduce heat to low, and cook for 40 to 45 minutes, or until the lamb is tender when pierced with a fork and the gravy has reduced to a thick, rich paste that clings to the meat.

While the meat is simmering, crush the saffron threads into the warm milk and set aside to steep. Ensure your basmati rice has been thoroughly rinsed 3 to 4 times to remove excess starch, then soak it in cold water for 30 minutes.

In a separate large pot, bring 2 liters of water to a boil along with the 2 tablespoons of salt, black cumin seeds, green cardamom, cloves, cinnamon stick, and bay leaf. Drain the soaked rice and add it to the boiling water. Cook on high heat for exactly 6 to 7 minutes. Test a grain: it should be long, bend slightly without snapping, and have a small, firm white core when pressed between your fingers (about 70% cooked). Drain the rice immediately through a colander and set aside.

Remove the pot of cooked lamb from the heat. Spread the lamb and its thick gravy evenly across the bottom of the pot. Sprinkle half of the reserved fried onions, half of the chopped mint, and half of the chopped coriander over the meat. Spread the drained, hot parboiled rice evenly over this herb layer. Drizzle the saffron-steeped milk, melted ghee, and kewra water (if using) evenly over the top of the rice. Finish by sprinkling the remaining fried onions, mint, and coriander.

Cover the pot tightly with a layer of aluminum foil, then press the lid firmly down over the foil to create an airtight seal. Place a flat griddle or tawa on your stove over medium heat for 3 minutes to heat up. Place the sealed biryani pot directly on top of the hot griddle, turn the heat to low, and steam-cook for 20 minutes.

Turn off the heat. Do not open the lid. Let the pot sit undisturbed on the warm griddle for 10 minutes to allow the steam to settle. Gently remove the lid and foil, and use a wide, flat spoon or saucer to scoop the biryani from the side of the pot, bringing up layers of spiced lamb, white rice, and yellow saffron rice without over-mixing or breaking the long grains.