Set the Instant Pot to the sauté mode. Add olive oil, and once hot, add diced onions, carrots, and celery. Sauté for about 5 minutes until the vegetables begin to soften.
Add minced garlic and sauté for an additional 1 minute until fragrant.
Season the chicken breasts with salt, pepper, thyme, and rosemary. Place them in the pot over the sautéed vegetables.
Add the rinsed wild rice and pour in the chicken broth. Stir gently to combine.
Close the lid of the Instant Pot, ensuring the valve is set to sealing. Select the manual or pressure cook setting and cook on high pressure for 25 minutes.
Once cooking is complete, allow for a natural pressure release for about 10 minutes, then perform a quick release for any remaining pressure.
Carefully remove the chicken breasts and shred them using two forks. Return the shredded chicken back to the pot.
Stir in the coconut milk (or heavy cream) and let the soup heat through for an additional 5 minutes on sauté mode.
Taste and adjust the seasoning if necessary, adding more salt or pepper if desired.
Serve hot, garnished with fresh parsley.
Notes
Adjust seasoning to taste and use coconut milk for a dairy-free option.