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, or until the vegetables start to soften and the onion becomes translucent.

2. Stir in the minced garlic and cook for another minute until fragrant.

3. Pour in the chicken broth and add the dried thyme. Bring the mixture to a gentle simmer, then reduce the heat to low, cover, and let it cook for 10 minutes to allow the vegetables to become tender and the flavors to meld.

4. Stir in the can of cream of chicken soup until it is fully dissolved and incorporated into the broth.

5. Add the cooked shredded or diced chicken and the cooked white rice to the pot. Stir gently to combine all the ingredients.

6. Pour in the heavy cream and stir well. Continue to cook on low heat for another 5 minutes, or until the soup is heated through and slightly thickened. Do not bring the soup to a rolling boil after adding the cream, as it can sometimes curdle.

7. Taste the soup and adjust the seasoning with salt and black pepper as needed. Ladle the hot soup into bowls and garnish with fresh chopped parsley, if desired, for a touch of freshness.