In a medium saucepan, combine wild rice and water. Bring to a boil, then reduce heat, cover, and simmer for 45 minutes or until rice is tender. Drain any excess water and set aside.
In a large pot or Dutch oven, melt butter over medium heat. Add onion, carrots, and celery. Sauté for 5–7 minutes until vegetables are softened.
Add garlic, thyme, rosemary, and bay leaf. Cook for 1 minute until fragrant.
Pour in chicken broth and add chicken breasts. Bring to a simmer and cook for 20 minutes, or until chicken is fully cooked.
Remove chicken from the pot and shred it using two forks. Return shredded chicken to the pot.
Stir in cooked wild rice and heavy cream. Simmer for 5–10 minutes to combine flavors. Season with salt and pepper to taste.
Remove bay leaf. Serve hot, garnished with fresh parsley.
Notes
For a richer flavor, use homemade chicken broth. Leftovers can be stored in the refrigerator for up to 4 days.