Press the 'Sauté' button on the Instant Pot and add the olive oil when the pot is hot.
Add the diced onion and sauté for about 3 minutes until translucent. Add the minced garlic and sauté for another minute until fragrant.
Add the sliced carrots and celery, stirring everything together and sautéing for another 2-3 minutes.
Place the chicken breasts in the pot, pour in the chicken broth, and stir in the thyme, parsley, black pepper, and salt. Ensure the chicken is submerged.
Close the lid of the Instant Pot, set the valve to 'Sealing,' and select the 'Pressure Cook' setting for 10 minutes at high pressure.
After the cooking time is complete, allow the pressure to release naturally for 10 minutes before switching to 'Venting' to release any remaining pressure.
Open the lid and carefully remove the chicken breasts. Shred the chicken using two forks and return it to the pot.
Add the egg noodles and frozen peas to the soup. Select the 'Sauté' setting and cook for about 5-7 minutes, or until the noodles are tender.
Taste the soup and adjust the seasoning as needed. Serve hot, garnished with fresh parsley if desired.