1. Stir saffron into broth; set aside. In a large Dutch oven, heat oil over medium-high heat. Add chicken in 2 batches and cook, turning, until browned, about 7 minutes per batch. Remove to a plate.
2. Add onion, carrots, and garlic to drippings in pan. Reduce heat to medium and cook, stirring often, until onion is softened, about 5 minutes. Stir in ginger, paprika, cumin, cayenne, reserved broth, and half of cilantro. Return chicken to pan along with any juices that have accumulated on plate. Reduce heat to medium-low, cover, and simmer until chicken is tender, 25 to 30 minutes. Remove chicken to a platter and cover to keep warm.
3. Stir couscous, lemon juice, lemon zest, olives, almonds, and remaining cilantro into liquid in pan. Cover and let stand over very low heat 5 minutes. Fluff with a fork. Serve with chicken.