In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until translucent.
Stir in the minced garlic, diced carrots, and celery. Cook for another 5 minutes until the vegetables begin to soften.
Add the dried thyme, dried rosemary, salt, and black pepper. Stir to combine and cook for 1 minute.
Pour in the chicken broth and bring the mixture to a boil.
Once boiling, add the cooked chicken and rice. Reduce the heat to low and simmer for about 15 minutes, or until the rice is tender.
Stir in the heavy cream and frozen peas. Cook for an additional 5 minutes until heated through.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley.