Melt 2 tablespoons of butter in a large Dutch oven or heavy-bottomed stockpot over medium heat. Add diced onion, carrots, and celery. Sauté for 6 to 8 minutes until vegetables soften and onions become translucent.
Stir in minced garlic and chopped fresh thyme. Cook for 60 seconds until fragrant, stirring constantly to prevent the garlic from browning.
Add the remaining 2 tablespoons of butter. Once melted, sprinkle the flour evenly over the vegetables. Cook, stirring vigorously, for 2 minutes to cook off raw flour starch.
Slowly stream in 6 cups of chicken bone broth while whisking continuously to dissolve the roux and ensure a silky base without lumps. Stir in the rinsed wild rice blend, sea salt, and black pepper.
Nestle whole raw chicken breasts gently into the broth. Bring liquid to a gentle boil, then immediately lower heat to low. Cover tightly with lid and simmer for 30 to 35 minutes, stirring occasionally, until rice is tender and chicken reaches 165°F internally.
Transfer cooked chicken breasts to a clean board and shred into bite-sized ribbons using two forks. Return shredded chicken to the pot.
Reduce heat to low. Slowly stir in heavy whipping cream and minced fresh rosemary. Allow soup to simmer uncovered for 3 to 5 minutes until rich and velvety. Adjust seasoning with additional sea salt and cracked pepper. Ladle warm into ceramic bowls and serve!