Wash and soak the rice: Rinse the basmati rice several times until the water runs mostly clear. Soak in salted water for at least 1 hour, then drain.
Bloom the saffron: Gently crush the saffron threads and combine them with 3 tablespoons of hot water. Let stand for 15–30 minutes.
Prepare the orange peel: Remove the colored outer peel from the oranges, avoiding the white pith. Cut the peel into thin strips. Blanch the peel once or twice to reduce bitterness, then drain.
Candy the orange peel: Place the blanched orange peel in a saucepan with water and sugar. Simmer gently until tender and lightly coated in syrup. Add rose water or cardamom near the end, if using.
Prepare the carrots and nuts: Sauté the carrot matchsticks in a little butter or oil until slightly tender. Add a little orange syrup and saffron if desired. Separately, lightly toast the almonds and pistachios. If using barberries, sauté them briefly with a little sugar.
Parboil the rice: Bring a large pot of salted water to a boil. Add the soaked rice and cook for several minutes, until the grains are tender on the outside but still slightly firm in the center. Drain and rinse gently.
Steam the rice and make tahdig: Add oil or butter to the bottom of a heavy pot. Add potato slices, bread, or a layer of rice for the tahdig. Add the parboiled rice in layers and make several holes with the handle of a wooden spoon. Cover with a clean kitchen towel and lid. Steam over low heat until the rice is fluffy and the bottom is golden and crisp.
Prepare saffron rice: Remove a small amount of cooked rice and mix it with the bloomed saffron until golden.
Assemble: Gently combine some of the rice with the carrots, candied orange peel, barberries, almonds, and pistachios. Transfer to a serving platter and garnish with the saffron rice and remaining toppings.
Serve: Serve warm with chicken, lamb, grilled meats, yogurt, fresh herbs, or salad. Serve the tahdig separately or arrange it around the platter.