Rinse the rice and soak in 4 cups of water for 20 minutes. Drain all the water after 20 minutes.
While the rice is soaking hard boil the eggs. Add 1 cup of water to the Instant Pot. Place the trivet and place eggs on top of it. Close the Instant Pot lid with pressure valve to sealing. Set the Instant Pot to pressure cook (hi) for 5 minutes. Allow 5 minutes of natural pressure release and then release the remaining pressure and open the Instant pot. Using a pair of heat resistant mitts, carefully pickup the Instant Pot insert and place it in the sink. Run cold water for 2 minutes over the eggs or place them in an ice bath. Once the eggs are cool to handle, peel them. Make 3 shallow slits to the hard boiled eggs and keep aside.
Set the Instant Pot to saute mode and add ghee. Add onions and saute until they turn light golden brown, about 10 minutes. Take half of the onions out and reserve.
Deglaze the bottom of the pot to remove any browning from sauteeing the onions. Use 1 to 2 tablespoons of water to help remove any stuck browned bits as this will help the Instant Pot come to pressure properly and not show the dreaded "BURN"
Add cumin seeds, black peppercorns, bay leaves and saute for a minute. Turn the Instant Pot off and add red chili powder, turmeric, salt, garam masala, ginger, garlic, mint, cilantro, tomatoes and yogurt. Mix well once again deglazing the pot.
Add eggs and mix coating the eggs with the spices. Add rice over and spread it evenly. Add water and stir gently making sure most of the rice is under liquids. Close the Instant Pot with pressure valve to sealing. Pressure Cook (Low) for 5 minutes followed by 5 minutes natural pressure release. Release the remaining pressure and open the Instant Pot. Layer the reserved caramelized onions and saffron milk evenly on top. Garnish with remaining cilantro. Enjoy hot with a lemon wedge and raita.
To make the raita, whisk the yogurt in a medium bowl. Add onions, tomatoes, salt, sugar and mix well. Garnish with cilantro.