Sauté Vegetables: In a large pot, heat the olive oil over medium heat. Add the diced onion, sliced leek, carrots, celery, and a pinch of salt. Sauté until the vegetables are softened, about 5-7 minutes.
Add Seasonings: Stir in the garlic, turmeric, and poultry seasoning, cooking until the mixture becomes fragrant, about 1 minute.
Simmer the Soup: Pour in the chicken broth and add the chicken. Bring the mixture to a gentle simmer, cooking until the chicken is fully cooked and tender, approximately 15-20 minutes.
Shred the Chicken: Remove the chicken from the pot, shred it with two forks, and return it to the pot.
Finish the Soup: Add the coconut milk, frozen peas (if using), and chopped parsley. Stir to combine and heat through, seasoning with salt and pepper to taste.
Serve: Ladle the soup into bowls, garnish with additional fresh parsley if desired, and enjoy warm.