Rinse the basmati rice under cold water until it runs clear. Soak the rice in a large bowl of cold, salted water for at least 30 minutes. Meanwhile, grind the saffron threads with a mortar and pestle, then dissolve in 3 tablespoons of hot water and set aside to bloom.

In a small pan over medium heat, add the julienned carrots, 2 tablespoons of sugar, and 2 tablespoons of water. Cook until the carrots are tender and glazed. In a separate pan, melt 1 tablespoon of butter, add the rinsed barberries and 1 tablespoon of sugar. Sauté for 1-2 minutes until plump. Combine the glazed carrots, barberries, toasted almonds, pistachios, and candied orange peel in a bowl.

Bring a large pot of salted water to a rolling boil. Drain the soaked rice and add it to the pot. Boil for 5-7 minutes until al dente (soft on the outside, firm inside). Drain immediately in a colander and rinse with lukewarm water.

In a large non-stick pot, heat the oil and remaining 3 tablespoons of butter over medium heat. Add two large scoops of the parboiled rice and mix with 1 tablespoon of the bloomed saffron water. Press this mixture firmly into the bottom of the pot to create the tahdig layer.

Gently pile the rest of the rice on top of the tahdig layer in a pyramid shape. Drizzle the remaining saffron liquid over the top of the rice mound in streaks. Poke 4-5 holes through the rice with the handle of a wooden spoon. Cover the pot with a lid wrapped in a clean kitchen towel and cook on low heat for 45-50 minutes, until the rice is fluffy and the tahdig is golden and crisp.

To serve, gently fluff the white and saffron rice and arrange it on a large serving platter. Sprinkle the jeweled topping mixture generously over the rice. Carefully remove the tahdig, break it into pieces, and arrange them around the rice. Serve immediately.