In a large skillet, melt 2 tablespoons ghee over medium heat. Add the onions and a pinch of salt; cook, stirring occasionally, until softened and starting to very lightly brown in places, about 25 minutes. Lower the heat to medium-low and cook, stirring occasionally, until the onions have released all of their juices and are deeply caramelized, 20–25 minutes more. Turn off the heat.
Meanwhile, in a fine-mesh colander, rinse the rice well, then transfer to a large bowl. Add enough cold water to cover by a few inches, then let soak for 30 minutes.
In a separate small bowl, add the saffron threads and a scant half cup of hot water; let soak.
Using a spice grinder or mortar and pestle, grind 10 cardamom pods, 10 cloves, 3 pieces of the cinnamon, the coriander, and the peppercorns into a powder. Transfer to a medium bowl and add 1½ teaspoons salt, the chili powder, the turmeric, and ½ cup yogurt; stir well to combine.
To a large platter or baking dish, add the chicken and rub all over with the yogurt mixture. Let marinate for 20 minutes, then add the potato pieces and let marinate another 20 minutes.
Meanwhile, boil the eggs: Bring a medium pot of water to a rapid boil. Carefully lower in the eggs, then cook 8–9 minutes. Drain, then transfer to a bowl of ice water to cool. Once cooled, peel, halve, and set aside.
In a large (8- to 10-quart), heavy-bottomed pot, heat ¼ cup ghee over medium-high heat until shimmering. Add 5 cardamom pods, 5 cloves, the bay leaves, and the remaining cinnamon pieces and cook until fragrant, 1–2 minutes. Remove the whole spices if desired. Add the marinated chicken pieces skin side down to the ghee and let cook 2 minutes. Add the potatoes, half of the caramelized onions, and the tomatoes. Cook, stirring occasionally, until the mixture looks saucy and the potatoes begin to soften, about 15 minutes.
Drain the rice and massage it with the remaining yogurt. Add to the pot with the chicken. Add the saffron and its soaking liquid, ½ teaspoon salt, and just enough water to barely cover the rice. Stir once, making sure the rice and potatoes are submerged, then reduce the heat to medium-low; cover and let cook, stirring once or twice to make sure that the rice isn’t scorching at the bottom (it may get a little crunchy), 20–25 minutes.
Meanwhile, in a small saucepan over medium-low heat, melt the remaining ½ cup ghee and add the remaining 5 cardamom pods and cloves and a pinch of salt. Let simmer gently to infuse the ghee with the spices’ flavor.
When the rice is cooked and potatoes are tender but not mushy, remove the pot from the heat. Taste and adjust the salt as needed. Stir some of the warm ghee mixture into the rice (discard the spices in the ghee). Transfer to a serving platter, arrange the remaining caramelized onions and the eggs on top, and drizzle each egg with the warm ghee. Sprinkle with the cashews and cilantro and serve.