Set your Instant Pot to the 'Sauté' mode and add the olive oil. Once the oil is heated, add the diced onion, carrots, and celery. Sauté for about 5-7 minutes until the vegetables are soft. Stir occasionally.
Add the minced garlic and sauté for an additional 1-2 minutes until fragrant.
Place the chicken breasts into the pot, followed by the chicken broth, dried thyme, dried rosemary, salt, and black pepper. Stir to combine.
Close the lid of the Instant Pot and ensure the steam release valve is set to sealing. Select the 'Manual' mode and set the timer for 15 minutes on high pressure.
Once the cooking time is complete, let the pressure release naturally for 10 minutes, then carefully switch the steam release valve to venting to release any remaining pressure.
When the pressure is fully released, remove the chicken breasts and shred them using two forks. Return the shredded chicken back to the soup.
Stir in the frozen peas and heavy cream. If you desire a thicker soup, whisk the flour with a little water to create a slurry, and then add it to the pot. Mix well and set to 'Sauté' mode for an additional 5 minutes to thicken the soup if desired.
Taste and adjust seasoning as necessary. Ladle the soup into bowls and garnish with chopped fresh parsley before serving.