Heat olive oil in a large pot over medium heat. Add the chopped onion, garlic, and ginger. Sauté for 5 minutes until softened and fragrant.
Add the chicken to the pot and cook for 5-7 minutes, until it’s browned on all sides.
Stir in the turmeric, cumin, and coriander, cooking for an additional 1-2 minutes to release the flavors of the spices.
Pour in the chicken broth and add the carrots and celery. Bring to a boil, then reduce heat and simmer for 20 minutes, or until the vegetables are tender and the chicken is cooked through.
Stir in the coconut milk (if using) and spinach or kale, cooking for another 2-3 minutes until the greens are wilted.
Add lemon juice, salt, and pepper to taste.
Serve hot, garnished with fresh cilantro.