In 6 qt Instant Pot add 3 tbsp olive oil and turn on sauté. As it warms up, salt & pepper each side of the boneless skinless chicken breasts. Add to the heated oil and sear each side for 4 minutes.
Then transfer the chicken breast to a clean plate. Pour 1/3 cup of white wine into the instant pot to deglaze it. Take spoon and scrape the bottom while deglazing to make sure nothing is sticking on the bottom.
Then add in chopped yellow onion & minced garlic. Sauté for 2 minutes.
After add in the chopped celery & carrots. Then season with the rosemary, parsley, salt, turmeric and cayenne pepper for 5 minutes. Take spoon and make sure nothing is stuck to the bottom, then add chicken breasts back into the Instant Pot on top.
Then pour in your chicken broth and wild rice. Stir & then place the thyme springs on top. Close Instant Pot lid & seal. High pressure cook for 25 minutes, then naturally release.
Take lid off once steam release valve has dropped and take thyme sprigs out to discard. Take chicken breasts out to rest for 10 minutes. While the chicken rests you will get the gluten free roux ready.
In frying pan you will add 1/4 cup butter to the pan, on medium heat you will let it melt, then add in 1/2 cup of the brown rice flour. Mix the flour into the butter and let cook for 1 minute.
Then start slowly adding the 2 cups milk of choice, whisking until no clumps. It will start to absorb the liquid pretty quickly. The consistency will end up being thick and smooth. After you will slowly add the roux into the Instant Pot and whisk it in gradually.
The roux will seem thick in the soup at first, but keep whisking then it will thin out and be fully incorporated. Shred the chicken by 2 forks or in the kitchen aid stand mixer.
After the chicken back into the soup, whisk until fully incorporated again, then once it is fully mixed in, sauté soup on low for 10 minutes. Then dig in!