This Arabian Gulf showstopper is traditionally prepared by stuffing a whole lamb with rice or pasta, nuts, onions, and spices. Martha simplifies the dish by using lamb shoulder instead.
Make the lamb: Pat lamb dry; generously season all over with salt and pepper. Grate 2 1/2 inches ginger and 2 garlic cloves into a small bowl. Add 1 pinch saffron, then rub mixture evenly over the inside of the lamb. Roll up lamb, with fat on the outside, and secure with kitchen twine. Heat 2 tablespoons oil in a Dutch oven or other large heavy-bottomed pot over medium-high. Add lamb bones and cook until browned, about 20 minutes. Add lamb and cook, turning occasionally, until browned on all sides, 8 to 10 minutes; transfer to plate along with bones. Wipe out any remaining fat with a paper towel.
Add onions and remaining 2 tablespoons oil to pot and cook until golden brown and softened, 10 to 12 minutes. Crush remaining 3 garlic cloves, slice remaining 1 inch ginger, and add both to pot along with lamb bones and meat, cardamom, cloves, bay leaves, cinnamon, peppercorns, and remaining 1 pinch saffron. Add just enough water to cover lamb. Bring to a boil; reduce to a simmer, cover, and cook until lamb is almost tender, about 2 hours. Discard bones.
Preheat oven to 325 degrees. Transfer lamb to a rimmed baking sheet or roasting pan. Strain cooking liquid and reserve. Combine ghee and tomato paste and season with salt. Brush ghee mixture all over lamb, then roast, brushing occasionally with juices, until fork-tender, 1 1/2 to 2 hours.
Make the rice and potatoes: Preheat oven to 450 degrees. Place rice in a bowl and add enough water to cover. Swirl water to rinse rice and drain. Repeat process 3 to 4 more times until water is clear. Cover rice with clean water and soak for 30 minutes, then drain.
On a rimmed baking sheet, toss potatoes with 2 tablespoons oil; season with salt and pepper. Arrange in a single layer and roast, tossing halfway through, until potatoes are tender when pierced with a knife, about 30 minutes. Before serving, rewarm potatoes in a 325-degree oven, if necessary.
Meanwhile, add rice to a large saucepan along with 3 1/2 cups reserved lamb cooking liquid. Season well with salt. Bring to a boil, cover, and simmer until rice is tender, about 15 minutes. Fluff with a fork.
In a small bowl, combine orange zest and juice. Whisk in mustard, vinegar, and remaining 4 tablespoons oil; season with salt and pepper. Drizzle dressing over arugula and toss to combine.
To serve, transfer rice to a large platter. Arrange potatoes over rice and top with arugula mixture. Place lamb in the center of the platter and sprinkle currants and pistachios on top. Garnish platter with clementines. Serve with remaining reserved lamb cooking liquid on the side.