Heat olive oil over medium heat in a large soup pot. Add onions, celery, carrots, ginger and garlic. Saute about 5 minutes, stirring frequently, until softened.
Add the chicken, broth, vinegar, red pepper, turmeric, salt and pepper.
Bring to a boil, then reduce heat to simmer. Cover and cook for about 20 minutes or until the chicken is cooked through. Remove the chicken and set aside to cool.
Add the broccoli to the pot and cook an additional 5 minutes. While cooking, shred the chicken and stir back into the soup.
Remove the pot from the heat and stir in the spinach and parsley. Adjust seasoning to taste.
Heat spiralized zucchini in a bowl in the microwave, just until warm. Divide heated zoodles into 6 bowls.
Ladle hot soup over zoodles and serve.