1. Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion, carrots, and celery. Cook, stirring occasionally, for 5-7 minutes until the vegetables start to soften.

2. Stir in the minced garlic, dried thyme, salt, and pepper. Cook for another minute until the garlic is fragrant.

3. Add the chicken broth and uncooked long-grain white rice to the pot. Bring the mixture to a boil, then reduce the heat to low, cover the pot, and simmer for 12-15 minutes, or until the rice is tender.

4. Once the rice is cooked, stir in the shredded or diced cooked chicken and the heavy cream. Continue to simmer gently for another 3-5 minutes, just until the soup is heated through and the cream is fully incorporated. Do not bring the soup to a rolling boil after adding the cream.

5. Remove the pot from the heat and stir in the fresh chopped parsley.

6. Taste the soup and adjust the seasonings if needed. Serve hot.