In a large bowl, cover the apricots with warm water and let stand for 1 hour; drain. In a medium bowl, cover the rice with water and let soak for 30 minutes; drain.

Meanwhile, in a medium saucepan, heat 1 inch of vegetable oil to 325 degrees. Add the onion slices and fry, stirring occasionally, until browned and crisp, about 7 minutes. Drain on paper towels.

In a large saucepan, toast the saffron over moderately high heat, 30 seconds. Transfer the saffron to a small bowl and let cool. Crumble the threads and add the milk.

In the same large saucepan, heat the 2 tablespoons of oil. Add the cumin seeds and cook over moderately high heat until fragrant. Add the garlic and 2 tablespoons of the ginger and cook over moderately high heat until the garlic is golden. Add the yogurt, cayenne pepper, and the 1 cup of water and simmer over low heat, stirring occasionally, for 5 minutes. Add the apricots, pistachios, and garam masala and simmer for 5 minutes, stirring occasionally. Season with salt.

Preheat the oven to 325 degrees. In another large saucepan of boiling salted water, cook the rice until al dente. Drain and return to the saucepan. Stir in half of the saffron milk, cover, and set aside. Add the remaining saffron milk to the pistachio-yogurt mixture.

Spread half of the pistachio yogurt in a large, deep casserole or Dutch oven. Drizzle 1 tablespoon of the melted butter over the yogurt and top with half of the chiles, fried onions, and 1 tablespoon of the ginger. Spread half of the rice in the casserole and drizzle with 1 tablespoon of the melted butter. Spread with the remaining pistachio-yogurt mixture, drizzle with 1 tablespoon of the butter and scatter the remaining chiles, fried onion, and 1 tablespoon of ginger on top. Cover with the remaining rice and drizzle on the remaining 1 tablespoon of melted butter. Cover the casserole tightly with foil, then cover with a lid.

Bake the biryani for about 15 minutes, until heated through. Uncover the biryani. Garnish with the chopped pistachios, mint, and cilantro and serve immediately.