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 black pepper. Cook for another minute until fragrant.
Add the uncooked wild rice and chicken broth to the pot. Bring to a boil, then reduce the heat to low. Cover and simmer for 45 minutes, or until the rice is tender.
Once the rice is cooked, stir in the shredded chicken and heavy cream. Cook for an additional 5 minutes to heat through.
Finally, add the frozen peas and cook for another 2-3 minutes. Adjust seasoning if necessary.
Serve hot, garnished with fresh parsley.