1/2 cup barberries soaked in cold water for 10 minutes
2 tablespoons brewed saffron
1/2 teaspoon cinnamon
small pinch of cumin
small pinch of coriander
2 tablespoons sugar, divided
1/4 cup slivered almonds
1/4 cup slivered pistachios
In a large bowl, cover the rice with cold water. Using your hand, agitate the rice to release the starch, then carefully pour off the water. Rinse the rice 5 to 7 more times, until the water runs clear. Cover the rice with water, add 2 teaspoons of salt and let soak for 30 minutes, then drain.
Fill a 5-quart nonstick Dutch oven half full with water, bring to a boil and add 2 tablespoons of salt. Add the rice and boil over high heat until it is al dente and just starts to soften; this can takes about 5-10 minutes, depending on your rice (do not overcook it). Let stand for 2 minutes, then drain well. Wipe out the pot.
Put the oil in the bottom of the Dutch oven. In a small bowl, whisk the yogurt with the egg yolk and 2 tablespoons of the brewed saffron and drizzle over the oil in the pot. Gently scatter one-quarter of the rice into the pot (you want it to stay fluffy).
Cover the pot and set it over moderately high heat until it starts to steam, about 5 minutes. Uncover the rice and drizzle with the remaining 2 tablespoons of brewed saffron and 1/4 cup of boiling water. Scatter the butter slices on top. Cover the pot with a clean kitchen towel, then cover tightly with the lid and secure towel around lid. Cook over moderately low heat until the rice is tender and very fragrant, about 45-50 minutes.
Before the rice is done, prepare the carrots and barberries. First heat olive oil and a dab of butter in a large skillet. Add carrots and sauce over medium heat until softened a bit about 5 minutes. Season carrots with cumin, coriander, cinnamon and 1 tablespoon of sugar. Stir to mix lower heat and place lid slightly ajar to capture steam and cook another 5 minutes. Set carrots aside and wipe skillet clean. Heat more olive oil in the skillet about 1 tablespoon and a dab of butter and add barberries. Saute the berries and add 1 tablespoon of sugar and saute over low heat for 1 minute and set aside.
When rice is ready, remove the kitchen towel. Please 2 spatulas of rice in a small dish and color with the 2 tablespoons of brewed saffron to color the rice. Set this rice aside for the moment. Remove the rice from the pot by the spoonfuls. You want to create layers of rice and layers of carrots and barberries. Repeat the rice layering and carrot barberry layering until you reach the tahdig at the bottom of the pot. Reserve the tahdig and serve on a separate platter. Take the reserved saffron rice and place it on top of the rice pile. Sprinkle with pistachios and almonds and serve.
NOTE: To brew saffron grind ½ Teaspoons saffron with a generous pinch of sugar and then add 4 tablespoons hot water and let ground saffron dissolve. Let stand 30 minutes before proceeding.