In the slow cooker, add chicken breast, diced carrots, diced celery, diced onion, cubed zucchini, chopped broccoli (if using), minced garlic, bay leaf, dried thyme, and chicken broth. Mix gently.

Cover and cook on low for 5-6 hours or on high for 3-4 hours.

Remove chicken breast from the slow cooker. Shred it with two forks and return to the pot.

Season the soup with salt and pepper to taste. Garnish with fresh parsley before serving.