Add the chicken, rice, onion, carrot, celery, garlic, sweet potato, chicken stock, and all seasonings to the CrockPot or Instant Pot. Season with ½ tsp salt and 1 tsp pepper. Stir well.
For CrockPot: Cover and cook on low for 5-8 hours or on high for 3.5-5 hours, until the rice is tender and chicken shreds easily. For Instant Pot: Seal and cook on manual mode for 10 minutes. Let pressure release naturally for 5 minutes, then manually release any remaining pressure.
When soup is nearly done, melt butter in a small pot over medium heat. Slowly whisk in flour and cook, whisking constantly, for 1 minute. Gradually add in milk while whisking constantly. Let simmer over medium-low heat until thickened. Whisk often.
Remove the chicken, shred, and return it to the soup. Stir in the cream mixture, discard bay leaves, and adjust seasonings. If the soup is too thick, add up to 1 cup of milk.
Garnish with fresh parsley or thyme and serve with hearty buttered bread.
