Press the sauté button on the Instant Pot and add the olive oil to the pot. Once the pot is hot, add the onion, carrots and celery and cook, stirring occasionally, until veggies start to soften, about 3 minutes. Stir in the garlic.
Press "Cancel" to turn off the Instant Pot.
Add the dried oregano, thyme, bay leaf, salt, pepper, broth and water to the pot. Stir. Nestle the chicken into the broth.
Close the Instant Pot lid and turn the valve to the sealing position. Pressure cook on high pressure for 7 minutes. The Instant Pot will take about 20 minutes to reach pressure and then the cook time will begin counting down.
When the cook time ends, allow the Instant Pot to naturally release for 10 minutes. Then, carefully release the remaining pressure by turning the steam release valve to the venting position using the handle of a long spoon.
When the pin drops down, open the Instant Pot lid. Remove the bay leaf and discard. Remove the chicken to a clean plate, bowl, or cutting board. Let the chicken rest for a few minutes and then shred the chicken.
Press "Cancel" to turn off the warm setting and then press "Saute." Add the noodles to the pot and let them simmer for about 5 minutes, until just tender. Turn the Instant Pot off.
Stir the shredded chicken back into the soup. Taste soup and season with additional salt and pepper as needed. Serve soup with fresh parsley, if desired.