Set your Instant Pot to 'Sauté' mode. Add olive oil and let it heat for 1-2 minutes.
Add the chopped onion, carrots, and celery to the pot. Sauté for about 3-4 minutes until they start to soften.
Stir in the minced garlic, dried thyme, rosemary, black pepper, and salt. Cook for an additional minute until fragrant.
Add the chicken breasts to the pot, followed by the chicken broth. Stir to combine.
Close the lid of the Instant Pot and make sure the valve is set to 'Sealing.' Set to 'Manual' or 'Pressure Cook' mode and cook on high pressure for 10 minutes.
Once the cooking time is up, allow for a natural release for 5 minutes, then carefully switch the valve to 'Venting' to release any remaining steam.
Carefully remove the chicken breasts, shred them using two forks, and return the shredded chicken to the pot.
Add the egg noodles to the pot and stir well. Close the lid and set the Instant Pot to 'Manual' or 'Pressure Cook' mode again for 5 minutes.
Once done, perform a quick release. Stir the soup until the noodles are well combined.
Serve hot in bowls, garnished with fresh parsley if desired.