Heat olive oil in a large casserole over medium heat. Add chopped onions, cover, and cook until soft and translucent, about 10 minutes.

Add chicken pieces, garlic, turmeric, ginger, salt, pepper, and saffron. Turn chicken occasionally to brown lightly, 10-15 minutes.

Pour in the water and place the tied coriander bouquet on top. Bring to a boil, cover, reduce heat to medium-low, and simmer until chicken is cooked through, about 50 minutes.

While chicken cooks, remove the flesh from the preserved lemons and discard it. Finely chop the preserved lemon skin.

Remove chicken and coriander bouquet from the pot. Discard the bouquet. Reduce the sauce over medium heat for about 20 minutes until most liquid evaporates, stirring occasionally.

Stir in the chopped preserved lemon skin and olives. Simmer over medium-low heat for 10 minutes. Return chicken to the pot to warm through. Serve hot with couscous or bread.