Step 1

Preheat oven to 350°. Spread pistachios on a rimmed baking sheet and toast until just beginning to brown, about 4 minutes. Transfer to a plate, let cool, then coarsely chop. Spread almonds on the same baking sheet and toast until golden brown, 5–8 minutes; let cool. Set nuts aside.

Step 2

Place rice in a fine-mesh sieve and rinse under cold water until water runs clear. Cook rice in a large pot of boiling salted water, stirring occasionally, until grains have lengthened but are still firm, 6–7 minutes; drain and rinse under cold water. Spread rice on another rimmed baking sheet; let cool.

Step 3

Meanwhile, using a vegetable peeler, remove zest from orange and thinly slice lengthwise (reserve flesh for another use). Bring sugar and 1 cup water to a boil in a medium saucepan, stirring to dissolve sugar. Add orange zest and carrots, reduce heat, and simmer, stirring occasionally, until carrots are tender, 15–20 minutes; drain and set aside (discard syrup).

Step 4

Combine barberries and raisins in a small bowl and cover with hot water; let soak 10 minutes. Drain and set aside. Place saffron in another small bowl and add 1/4 cup hot water; set aside.

Step 5

Heat butter and 1 tablespoon oil in a large skillet over medium heat. Add onion, season with salt, and cook, stirring often, until soft and beginning to brown, 8–10 minutes. Add cardamom, cumin, turmeric, and 1 tablespoon saffron mixture. Cook, stirring constantly, until fragrant, about 1 minute.

Step 6

Reduce heat to low, add barberries and raisins, and cook, stirring often, about 3 minutes. Stir in reserved nuts and orange zest and carrot mixture; season with salt. Set fruit and nut mixture aside.

Step 7

Heat remaining 3 tablespoons oil in a large wide heavy pot over medium heat. Add half of rice, spreading evenly; top with fruit and nut mixture, then remaining rice, spreading evenly. Using the end of a wooden spoon, poke 5–6 holes in rice all the way through to bottom of pot (to help release steam and help rice cook evenly).

Step 8

Drizzle remaining saffron mixture over rice. Place a clean kitchen towel over pot, cover with a tight-fitting lid, and secure loose edges of towel on top of lid, using a rubber band or masking tape.

Step 9

Cook until pot begins to steam, 5–8 minutes. Reduce heat to very low and cook, without stirring, until rice is tender and bottom layer of rice is browned and crisp, 30–40 minutes.

Step 10

Scoop rice into a wide serving bowl, breaking bottom crust into pieces.

Step 11

DO AHEAD: Fruit and nut mixture can be made 2 days ahead. Cover fruit and nut mixture and remaining saffron mixture separately and chill.