Heat 6-quart Instant Pot to Sauté. Add oil, carrots, celery, onion, salt and pepper. Cook, stirring frequently, until onions are translucent.
Add broth, water, chicken, thyme, bay leaf, and rosemary. Secure lid and turn valve to seal. Set Instant Pot on Pressure Cook (or Manual, High Pressure) for 11 minutes. Quick release pressure when done cooking.
Remove chicken to a plate, and remove and discard bay leaf and rosemary sprig.
Turn Instant Pot back to Sauté. When soup comes to a boil, add noodles and continue to cook, stirring occasionally, until noodles are tender, or about 7 to 8 minutes (check the package for exact cooking time).
Meanwhile, shred chicken with two forks and return to pot when shredded.
When noodles have finished cooking, add peas and parsley and stir to combine. Taste and adjust seasoning for salt and pepper. You may also add more chicken broth or water if the soup is thicker than you like it.
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Notes
This recipe also works well with whole wheat pasta or another pasta of your choice (not gluten-free or chickpea pasta which may foam too much).
If you use low sodium or unsalted broth, you may have to add extra salt. Be sure to taste the soup before serving; adjust the seasoning if needed. Nutrition information is calculated with low sodium broth.