Spread the pistachios evenly on the baking sheet and toast in the oven until they just start to brown, about 4 minutes. Transfer to a plate to cool, then repeat with the almonds. Coarsely chop the pistachios.
While the nuts are toasting, rinse the basmati rice in a fine mesh strainer until the water runs clear. Soak in a bowl of water for about 10 minutes, then drain well. Put the rice in the 6-quart pot and cover with water. Add the kosher salt and bring to a boil, then reduce heat to medium and continuing cooking until the grains have lengthened but are still firm, about 6 to 7 minutes. Drain and rinse well with cold water. Spread the rice on the baking sheet and allow to cool.
While the rice cooks, combine the sugar with 1 cup of water in the medium saucepan and bring to a boil, stirring to dissolve the sugar. Add the carrots and orange zest, then reduce heat to a simmer. Cook, stirring occasionally, until the carrots are tender, about 15 to 20 minutes. Drain and reserve the carrots.
While the carrots cook, put the cranberries, currant, and chopped dates in a small bowl and cover with hot water. Allow to soak until they are soft, about 10 minutes, then drain. Soak the saffron in ¼ cup hot water.
In the skillet, heat the butter and 1 tablespoon olive oil over medium heat. Add the onion and sea salt, and cook until soft and starting to brown, about 8 to 10 minutes. Add the cardamom, cumin, turmeric, and 1 tablespoon of the saffron mixture. Stir and allow the mixture to release its fragrance, about 1 more minute. Stir in the drained fruits and continue cooking about 3 more minutes. Stir in the nuts and carrot mixture, and stir in another pinch of salt.
Heat 3 tablespoons of olive oil in the 6-quart pot over medium heat. Add half the rice, spreading it evenly. Top with the fruit and nut mixture, then spread on the remaining rice. Use the end of a wooden spoon to poke 5 or 6 holes in the rice all the way to the bottom of the pot. This helps release steam and allow the rice to cook evenly. Drizzle the remaining saffron mixture all over the rice.
Cover the pot with a large paper towel and put on the lid. If the towel lays over too far, trim the ends. Cook over medium-high heat until the pot starts to steam, about 5 to 8 minutes. Reduce heat to very low and cook until the rice is tender and the bottom rice has a crispy crust, about 30 to 40 minutes. Do not take off the lid as this will release the steam.
Scoop the finished rice into a large serving bowl, and break the crusty bottom into pieces.