Cook basmati rice in lots of water along with bay leaves, cloves, cinnamon, cardamom, marathi mogga, elaichi, mint leaves, oil and salt till its half cooked. Strain the water and spread the rice on a large wide plate. Allow to cool.
Heat 1 1/2 tbsps oil + 1 1/2 tbsps ghee in a vessel, add sliced onions, saute for 8-10 mts till caramelized. Remove half of the caramelized onions and keep aside.
To the remaining half caramelized onions, add green chillis, mint leaves, coriander leaves and ginger garlic paste and saute for 2 mts. Add red chilli pwd, coriander pwd and biryani masala pwd and salt (just enough for the egg masala) and combine well. Add chopped tomatoes and saute for 3 mts. Add the eggs and saute till well coated with the masala. (You can also halve the eggs and place carefully and saute in the masala).
Add the yogurt and combine. Cook for 5 mts till oil separates. Add lemon juice and combine. Turn off heat and keep aside.
Take a wide deep vessel to prepare the biryani. Add drizzle some oil all over, add half the rice as a first layer followed by the egg masala and spread out in the vessel.
Spread the remaining rice over the egg masala layer, pour 1/2 tbsp of ghee all over the rice, add the caramelized onions. Next sprinkle coriander leaves and pour the saffron milk over the rice.
Place lid and over the lid place a heavy weight. Cook on medium high flame for 5 mts. Remove the vessel from fire and place a iron tawa over low flame. Place back the vessel on the iron tawa and cook on low flame and cook biryani for 15 mts. Turn off heat and do not remove lid for 5 mts.
Remove lid, combine gently and serve hot with raita and curry of your choice.