Sprinkle the saffron into 1/4 cup hot water; let sit 15 minutes. Meanwhile, combine 2 cups water, the sugar and a pinch of salt in a small saucepan and bring to a boil. Add the orange zest and carrot, reduce the heat to medium low and simmer until tender, about 4 minutes. Drain and transfer to a bowl; set aside.
Heat 2 tablespoons butter in a large pot over medium heat. Add the onion, cinnamon stick, cardamom, allspice, cumin and a pinch of salt and cook, stirring occasionally, until the onion is translucent, about 8 minutes. Add the rice and 3/4 teaspoon salt and stir to coat. Add 3 cups water, increase the heat to medium high and simmer until the water has mostly evaporated, about 4 minutes. Cover the pot with foil and the lid, reduce the heat to low and cook until the water is completely absorbed, about 12 minutes. Remove from the heat and let stand 5 minutes.
Meanwhile, melt 1 tablespoon butter in a medium skillet over medium-high heat. Add the pistachios and almonds and cook until just lightly golden, about 1 minute. Remove from the heat and add the dried cranberries and apricots, and 1 tablespoon of the prepared saffron water; stir to combine, then transfer to a bowl and set aside for topping.
Uncover the rice and fluff with a fork; discard the cinnamon stick and cardamom pods. Transfer about half of the rice to a serving bowl. Add the remaining saffron water, 1 tablespoon butter and the reserved orange peel and carrot to the rice in the pot and stir gently. Add the yellow rice to the white rice and gently toss; sprinkle with the pistachio mixture and parsley.