In a bowl, whisk together 2 tablespoons olive oil, minced garlic, minced ginger, cumin, turmeric, 1/2 teaspoon salt, and 1/2 teaspoon black pepper to make the marinade.
Place the chicken fillets in a zip-top bag or shallow dish and pour the marinade over them, turning to coat evenly.
Marinate the chicken at least 4 hours or overnight in the refrigerator for best flavor.
Heat 2 tablespoons olive oil in a large skillet or Dutch oven over medium-high heat.
Sauté the chopped onion until soft and translucent, about 5–7 minutes.
Add the marinated chicken to the pan and cook just until the exterior turns white, about 2 minutes per side.
Pour in 3/4 cup chicken broth and any remaining marinade from the bag, bring to a boil, then reduce heat to low.
Cover and simmer for 20 minutes, turning the chicken once after 10 minutes.
Stir in the chopped preserved lemon peel, chopped parsley, chopped cilantro, and olives, then cover and simmer another 15 minutes.
Stir in the lemon juice, adjust seasoning with salt and pepper to taste, and serve immediately.