Season the chicken breasts generously with coarse salt and pepper on both sides.
In a large pot, heat the olive oil over high heat. Wait until it begins to smoke lightly, indicating it's hot enough. Carefully add the seasoned chicken breasts.
Reduce the heat to medium and let the chicken cook for about 3 to 4 minutes until nicely browned on one side.
Flip the chicken over, turn the heat down to low, and cook for an additional 5 minutes.
Once cooked, remove the chicken from the pot and let it rest. After a few minutes, large dice it and set it aside.
Add the diced carrots, celery, onion, and garlic to the same pot. Sweat the vegetables over low heat for about 8 to 10 minutes.
Return the diced chicken to the pot along with the wild rice and chicken stock. Ensure everything is well combined.
Cover the pot and let it cook over low heat for approximately 25 minutes, or until the wild rice is cooked through.
In a separate bowl, whisk together the cornstarch and cold water until smooth. Gradually mix this slurry into the soup, then raise the heat to high, bringing it to a boil.
Once thickened, turn off the heat and finish the soup by stirring in the heavy whipping cream, parsley, and adjusting the salt and pepper to taste.
