How to Make It
Drain and rinse the chickpeas. In a medium saucepan, cover the chickpeas with 1 inch of fresh water and bring to a boil. Reduce the heat to low and simmer, stirring occasionally, until tender, about 1 hour. Drain the chickpeas. Cover and set aside.
Meanwhile, in a large enameled cast-iron casserole, heat 3 tablespoons of the oil until shimmering. Add 3 tablespoons of the butter and, once it melts, add the chicken and brown well on all sides over moderately high heat. Transfer the chicken to a platter and add the lamb shanks to the casserole. Brown the lamb shanks on all sides and add them to the chicken. Add the pearl onions to the casserole and cook over moderately low heat, stirring occasionally, until golden brown, about 20 minutes. Transfer to a bowl. Pour the fat from the casserole.
Add 6 cups of water to the casserole along with the cinnamon sticks, bay leaves and 1 tablespoon of salt. Return the chicken and lamb shanks to the pot and bring to a boil. Cover and simmer over low heat, skimming as necessary, until the chicken is cooked through, about 1 hour. Transfer the chicken to a plate and pull off all the meat in as large pieces as possible. Cover the chicken with foil. Continue to simmer the lamb shanks until tender, about 40 minutes longer.
Meanwhile, put the couscous in a large heatproof bowl and toss with 1 tablespoon of the olive oil. Pour in enough boiling water to cover the couscous by 1 inch. Cover and set aside for 45 minutes.
When the lamb is done, strain the cooking liquid and skim the fat from the surface; you should have about 6 cups. Remove the meat from the shanks and cut it into 1-inch pieces.
In a medium saucepan, combine the lamb with the pearl onions, chickpeas, 1 teaspoon each of cinnamon and cumin, a large pinch of salt and 2 cups of the reserved cooking liquid. Cover and simmer over moderately low heat until the onions are tender and the liquid is flavorful, about 25 minutes. Stir in 1/3 cup of the cilantro.
Drain the couscous. In a large saucepan, melt the remaining 1 tablespoon of butter in the remaining 1 tablespoon of oil. Add the couscous, the remaining 1 teaspoon each of cinnamon and cumin and a pinch of salt. Cook over moderate heat, stirring, until most of the butter has been absorbed, about 3 minutes. Stir in the remaining 4 cups of the reserved cooking liquid and bring to a boil. Cover and simmer over low heat until the couscous is very tender and most of the liquid has been absorbed, about 30 minutes.
Meanwhile, preheat the oven to 350°. Put the chicken in a baking dish and add a little water. Cover and bake just until warmed through, about 10 minutes. Reheat the lamb stew. Mound the couscous on a large platter and arrange the chicken on top. Spoon the lamb stew over all and sprinkle with the remaining 2 tablespoons of cilantro. Serve at once with lemon wedges and pita triangles.