PRESS the SAUTE mode button on the Instant Pot. When HOT appears on the display, add butter and heat with the Instant Pot lid open until it begins to melt.
Add diced onion and cook for 1 minute, stirring occasionally.
Add in the celery, carrots, and garlic. Continue to cook for another 2 to 4 minutes or until vegetables are softened.
Press the CANCEL button to turn off saute mode..
Add ½ cup of the broth. Deglaze the pot by scraping the bottom to remove any browned bits.
Add the wild and brown rice, chicken, mushrooms, fresh thyme, bay leaves, dried sage, and dried rosemary.
Pour the remaining broth into the pot.
Close and lock the lid and set the valve in the SEALING position. Pressure cook on HIGH for 32 minutes.
Once it finishes cooking, allow to naturally release for 5 minutes, then turn the valve to quick release any additional steam.
Carefully open the Instant Pot lid. Remove the bay leaves and thyme sprigs and discard.
Remove the chicken and shred with a fork. Return to the pot.
Add the kale and push down into the broth.
Add the heavy cream and stir well. Allow to simmer for 1 to 2 minutes or just until heated through.
Season with salt and pepper as needed. Serve hot.