Soak the currants in a bowl of water for 10 minutes until swollen. Put the barberries in a separate bowl of water and soak for 5 minutes. Drain both and pat dry separately. Set aside.
Peel the orange, removing all the pith. Cut the peel into very thin strips, then transfer to a small saucepan. Add enough cold water to cover, then bring to the boil over a medium heat. Blanch for 20 seconds, then drain. Repeat the blanching twice more to remove the bitterness.
Reserve 1tablespoon each of the almonds, pistachios and soaked currants and combine the remainder with the blanched orange strips, then mix in the mint. Set aside.
Heat the oil in a heavy-based saucepan over a medium heat until it is sizzling. Using a spoon, sprinkle 4–5tablespoons of the rice across the bottom to cover the base. Sprinkle 1tablespoon of the fruit and nut mixture over the top, then sprinkle in apinch of advieh. Continue adding layers of rice, fruit and nut mixture and advieh, building the mixture up into a dome. Finish with a layer of rice. Avoid tipping all the rice in at once, as this will compress it, and the result will not be light.
Using the handle of a wooden spoon, make three holes in the rice all the way to the bottom of the pan. This forms the tahdeeg, or crispy base.
Melt half the butter in a small pan. Add the saffron liquid and 2tablespoons water and mix well. Pour the mixture over the rice.
Wrap the saucepan lid in a clean dish towel and tie it into a tight knot at the handle, then use it to cover the pan as tightly as you can so that steam does not escape. (The dish towel will prevent the moisture from dripping into the rice, making it soggy.) Cook the rice over a medium heat for 2–3 minutes until the rice is steaming (you will see puffs of steam escaping at the edges of the lid), then reduce the heat to low and cook, covered, for 20–25 minutes.
Meanwhile, melt the remaining butter in a small heavy-based saucepan over a medium heat, add the soaked barberries and fry, stirring often, for 3–4 minutes to refresh their colour. Remove from the heat and set aside for serving.
Serve the rice and tahdeeg following the instructions in steps 5–7 for Steamed Rice. Decorate the rice with the soaked barberries and the reserved almonds, pistachios and currants.