Place the rinsed wild rice blend in the bottom of the crock pot.
Add the chopped onion, minced garlic, diced carrots, and diced celery on top of the rice.
Place the chicken breasts on top of the vegetables and rice.
Pour in the chicken broth and water over all the ingredients in the crock pot.
Sprinkle the dried thyme, dried parsley, salt, and black pepper evenly over the top.
Cover the crock pot and cook on high for 4 to 4.5 hours, or until the chicken is cooked through and the rice is tender.
Once cooked, carefully remove the chicken breasts from the crock pot and place them on a cutting board.
In a small bowl, mix the all-purpose flour with the unsalted butter until it forms a smooth paste (a beurre manié).
Shred the chicken breasts using two forks and return the shredded chicken to the crock pot.
Stir the beurre manié into the crock pot to thicken the broth, mixing well.
Pour in the heavy cream and stir to combine.
Cover and cook on high for an additional 10 to 15 minutes until the broth has thickened and is creamy.
Taste and adjust seasoning with additional salt and pepper if desired.
Serve hot, spooning the chicken, wild rice, and creamy broth into bowls.