Rinse the wild rice and place in the Instant Pot with the chicken, onion, carrot, celery, broth, sage, thyme, rosemary, salt, and pepper. Set the pot to manual mode with high pressure and set the timer for 35 minutes. Allow the pressure to release naturally for 10 minutes before releasing the pressure manually and removing the lid.
Remove the chicken and shred using a fork. Return the chicken to Instant Pot along with the Greek yogurt. Stir until the soup is smooth. Ladle into serving bowls and top with parsley. Serve and enjoy!
If the soup needs thickening, combine the optional cornstarch and cold water. Stir until smooth and then gradually add to the soup until desired consistency is reached.