Set the Instant Pot to 'Sauté' mode and heat the olive oil. Once hot, add the diced onion and sauté for about 3 minutes until soft and translucent.
Add minced garlic, sliced carrots, and celery to the pot, continuing to sauté for an additional 2 minutes.
Stir in dried thyme, oregano, and black pepper, allowing the spices to toast briefly for about 30 seconds.
Pour in the chicken broth, scraping any bits stuck to the bottom of the pot. Add the shredded chicken, and bring the mixture to a simmer.
Secure the lid on the Instant Pot and set the valve to 'Sealing.' Pressure cook on 'High' for 7 minutes.
Once the cooking time is complete, do a quick release of the steam by carefully turning the valve to 'Venting.'
After all the steam has escaped, open the lid and stir in the egg noodles. Set the pot to 'Sauté' mode again, cooking for an additional 5-7 minutes until the noodles are tender.
In the last minute of cooking, add the frozen peas and let them warm through. Taste the soup and season with salt as desired.
Ladle the soup into bowls and garnish with fresh parsley before serving.