Heat oil in a 6- to 8-qt. heavy-bottomed pot over medium-high heat. Add half the chicken, skin side down, and cook until golden brown, 5 to 7 minutes. Turn over and cook 3 minutes more. Transfer to a plate; repeat with remaining chicken and set aside.
Drain all but 2 tbsp. oil from pot and reduce heat to medium. Add onion and sauté until golden, 5 to 7 minutes. Add garlic and ginger and cook, stirring constantly, for 3 minutes. Add cinnamon, turmeric, coriander, black pepper, cardamom pods, chiles, and salt and stir to combine. Return chicken to pot and add apricots, prunes, 2 cups chicken broth, and parsley sprigs. Bring mixture to a boil, then reduce heat to medium-low. Cover and simmer 40 minutes. Take pot off heat and remove parsley sprigs and chiles. Remove skin from chicken.
In a covered medium saucepan, bring remaining 2 cups chicken broth to a boil. Turn off heat, stir in couscous, cover, and let sit 5 minutes. Uncover pan and fluff couscous with a fork. Stir in 2 tbsp. minced parsley, pine nuts, and lemon zest and toss to combine. Mound couscous on a platter. Top with chicken thighs and pour sauce over the chicken. Sprinkle with remaining 2 tbsp. parsley.
Note: Nutritional analysis is per serving.