Slow Cooker Method (or Dutch Oven): Place the raw chicken breasts, rinsed wild rice blend, diced carrots, celery, onion, minced garlic, thyme, rosemary, bay leaves, salt, and pepper into your slow cooker (or a 6-quart enameled Dutch oven). Pour in the chicken bone broth and stir gently.
Cook Low and Slow: Cover and cook on LOW for 6 to 7 hours or on HIGH for 3.5 to 4 hours, until the wild rice has blossomed and is tender with a nutty bite, and the chicken registers 165°F (74°C).
Shred the Chicken: Transfer the cooked chicken breasts to a cutting board. Shred into tender bite-sized pieces using two forks, then return the shredded chicken back to the slow cooker.
Prepare the Creamy Roux: In a small saucepan over medium heat, melt the 4 tablespoons of butter. Whisk in the flour and cook for 1 to 2 minutes until golden and bubbling. Gradually ladle in 1 cup of hot broth from the soup while whisking vigorously to create a smooth, velvety paste. Whisk in the heavy cream until smooth.
Combine and Simmer: Pour the velvety cream mixture into the slow cooker, stirring thoroughly to combine. Discard the bay leaves. Cover and cook on HIGH for an additional 15 to 20 minutes until the soup thickens into a rich, luxurious consistency.
Season and Serve: Taste and adjust seasoning with additional sea salt and cracked black pepper if desired. Ladle into warm rustic bowls, garnish with extra fresh thyme leaves, and serve with warm artisan sourdough bread.