Dice onion, carrots, and celery into uniform pieces. Mince garlic, pat chicken dry with paper towels, and rinse wild rice under cold water until water runs clear.
Place onion, carrots, celery, garlic, wild rice, and chicken breasts in slow cooker. Add bay leaves, thyme, parsley, garlic powder, onion powder, pepper, and salt, then pour chicken broth over everything and stir gently.
Cover and cook on LOW for 6-8 hours or HIGH for 3-4 hours until chicken reaches 165°F and rice is tender. Avoid lifting lid during cooking.
Remove chicken breasts with tongs, place on cutting board, and shred into bite-sized pieces using two forks. Remove and discard bay leaves from slow cooker.
In a medium saucepan over medium heat, melt butter completely. Add flour and whisk constantly for 2-3 minutes until smooth and lightly golden.
Slowly pour milk into roux while whisking constantly, then add heavy cream and whisk until combined. Cook for 3-5 minutes, whisking frequently, until mixture thickens and coats the back of a spoon.
Slowly pour creamy mixture into slow cooker while stirring constantly. Add shredded chicken back in and stir thoroughly to combine. Let sit on WARM for 10-15 minutes, then taste and adjust seasoning.
Ladle hot soup into bowls and garnish with fresh chopped parsley if desired. Serve immediately.