Carefully remove the skin from the chicken. If your chicken breasts are very large (more than 1 pound each), use a very sharp knife to carefully slice them in half crosswise through the bone. Set aside.
Turn your Instant Pot to the sauté setting. Add the olive oil and butter.
Once the butter is melted, add the onion, carrots, and celery. Cook for 3 to 5 minutes, stirring often, until the onion softens and becomes translucent.
Stir in the salt, pepper, and oregano. Place the thyme and bay leaf on top. Pour in the chicken broth and 3 cups water. Gently add the chicken pieces.
Close and seal the Instant Pot. Cook on high pressure (manual) for 10 minutes. Let the pressure release naturally for 10 minutes, then immediately vent to release any remaining pressure. Carefully open the lid.
Remove the chicken and transfer it to a cutting board. Pick out the thyme stems and bay leaf and discard. Turn the Instant Pot to saute (you will need to press “cancel” first).
Add the noodles. Let cook, uncovered, until noodles are al dente, about 5 to 6 minutes.
While the noodles cook, shred the chicken and discard the bones. Once the noodles are done, turn off the Instant Pot. Stir in the parsley and shredded chicken. If you’d like a more brothy, thinner soup, stir in additional water until your desired consistency is reached. Taste and adjust seasoning as desired. Enjoy hot with an extra sprinkle of fresh parsley.