Soak biryani rice for 20 minutes. Drain. Set aside.
Make few slits on the eggs. To marinate eggs, place them in a bowl, and add yogurt, ground turmeric, garam masala and red chili powder. Toss well. Set aside.
To make the biryani masala powder, place cloves, cinnamon, cardamom, cumin seeds and black peppercorns in a spice grinder or mortar and pestle. Grind to a coarse powder. Set aside.
To cook rice, place a large saucepan over medium-high heat. Heat oil. Add bay leaf, cinnamon stick and cloves. Sauté, stirring constantly, for a minute. Pour in water. Add cardamom powder and lemon juice. Season with salt. Stir. Increase heat to high. Bring the mixture to a boil. As soon as water comes to a boil, add rice. Stir gently. When cooked (do not overcook rice), drain and set aside. (Make sure all the water from the rice is drained out completely)
To make saffron milk, place saffron and milk in a small bowl. Stir. Set aside for 10 minutes.
To make egg biryani, heat 1 teaspoon ghee and 1 tablespoon oil in a large casserole over medium-high heat. Add onions, and sauté for 3-4 minutes or until browned. Drain on an absorbent towel. Set aside. Add raisins, and fry until they are plump. Drain on an absorbent towel. Set aside. Add cashew nuts. Fry until browned. Drain on an absorbent towel. Set aside.
Heat 2 tablespoon oil or ghee to the same casserole. Add cumin seeds, bay leaf, cloves, cardamom pods and cinnamon, and fry for a minute. Add onions, and sauté, stirring occasionally, for 2-3 minutes or until they turn golden brown. Add ginger and garlic. Saute for a minute. Stir in green chilies, mint leaves, coriander leaves, yogurt, biryani masala powder, ground turmeric, ground coriander, garam masala and red chili powder. Saute for 2-3 minutes. Season with salt and pepper.
Spread rice on top the prepared masala. Pour in saffron milk. Drizzle with ghee.
Cover with tight lid. Place the pan over low flame and cook (in other words “dum”) for 10-12 minutes.
Transfer egg biryani to a serving dish. Place eggs on top.
Garnish with fried onions, cashew nuts and raisins. Serve with raita, pickle and pappadums.