Press the Sauté button on the Instant Pot and add the olive oil. Once hot, add the onion, carrots, and celery. Cook, stirring occasionally, for about 3 minutes, until the vegetables start to soften. Stir in the garlic and cook for 30 seconds. Press Cancel to turn off the Instant Pot.
Add the dried oregano, thyme, bay leaf, salt, pepper, and broth to the pot. Stir to combine. Nestle the chicken breasts into the broth.
Close the Instant Pot lid and set 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 before the cooking time begins.)
When the cook time ends, allow a natural release for 10 minutes. Then, carefully release the remaining pressure by turning the steam release valve to venting using the handle of a long spoon.
Once the pressure pin drops, open the Instant Pot lid. Remove and discard the bay leaf. Transfer the chicken to a plate or cutting board and let it rest for a few minutes before shredding.
Press Cancel to turn off the warm setting, then press Sauté. Add the egg noodles and let them simmer for about 5 minutes, until just tender. Turn off the Instant Pot.
Stir the shredded chicken back into the soup. Taste and adjust seasoning with additional salt and pepper, if needed. Serve warm, garnished with fresh parsley, if desired.