Set instant pot to the sauté setting. Add olive oil, carrots, onion, celery, and garlic. Cook for 3 to 5 minutes, stirring so the garlic does not burn.
Add chicken broth, water, quartered parsnip, and seasonings. Stir to combine.
Carefully drop in the chicken thighs.
Cover the instant pot. Set the valve to the "sealing" position. Pressure cook on high for 10 minutes.
Once the timer is up, allow pressure to naturally release for 10 minutes before switching the valve to the "venting" position and manually releasing any remaining pressure.
Remove the chicken to a cutting board. Remove and discard the bay leaf and parsnip quarters.
Remove the chicken from the bone. Discard any skin, bones, and cartilage.
Once again, set the instant pot to the sauté setting. Add the rice to the broth and simmer 8 to 10 minutes until the rice is tender.
Add chicken back to the pot, along with any additional water, salt, or pepper (to taste). I usually add around another 1 cup of water to make more broth.
Notes
Make sure your instant pot is large enough to handle more than 8 cups of liquid or adjust the recipe to fit the size that you have.
If you prefer a less greasy soup, you can store the soup in the refrigerator overnight before serving. Then, skim the solidified fat off the top and warm to serve.
If you'd like to make chicken noodle soup instead, simply leave out the rice and cook wide egg noodles instead. Use about ½ a bag of wide egg noodles and cook for about 5 to 6 minutes in the broth, until tender.