Set the Instant Pot to ‘Sauté’ mode and heat the olive oil.
Add the diced onion, sliced carrots, and sliced celery to the pot. Cook, stirring occasionally, for 4-5 minutes until the vegetables begin to soften.
Add the minced garlic and cook for an additional 1 minute until fragrant.
Pour in the chicken broth and stir in dried thyme, dried parsley, dried rosemary, black pepper, and salt.
Place the chicken breasts into the broth, ensuring they are submerged.
Close the Instant Pot lid and set the valve to ‘Sealing’. Cook on ‘Manual’ or ‘Pressure Cook’ high pressure for 10 minutes.
When the cooking cycle ends, allow a natural pressure release for 10 minutes, then carefully quick release any remaining pressure.
Open the lid and remove the chicken breasts. Shred the chicken using two forks and set aside.
Turn the Instant Pot back to ‘Sauté’ mode. Add the egg noodles to the broth and cook for 5-6 minutes, stirring occasionally, until the noodles are tender.
Return the shredded chicken to the pot and stir to combine. Heat through for 1-2 minutes.
Stir in the chopped fresh parsley.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve hot.