In a large pot, heat the olive oil over medium heat. Add the diced onion, carrots, and celery. Sauté for about 5 minutes until the vegetables are softened.
Stir in the minced garlic, thyme, rosemary, salt, and pepper. Cook for an additional minute until fragrant.
Pour in the chicken broth and bring to a boil. Add the rinsed wild rice, reduce the heat to low, and cover. Simmer for about 45 minutes, or until the rice is tender.
Once the rice is cooked, stir in the shredded chicken and heavy cream. Heat through for about 5 minutes.
Add the frozen peas and cook for another 2-3 minutes until heated.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley.