In a large Dutch oven, melt butter over medium heat.
Add diced carrots, diced celery, diced onions, and minced garlic to the melted butter.
Sauté the vegetables for about 5 minutes or until they start to become tender.
Sprinkle the flour over the vegetables and stir to coat them all. Cook for 2-3 minutes.
Pour the chicken broth into the dutch oven and mix, scraping the bottom of the pot to remove any stuck pieces of flour or vegetables.
Add the chicken, sea salt, black pepper, rosemary, and bay leaf and cover.
Reduce heat to medium low and simmer for 15-20 minutes to cook the chicken, stirring every 5 minutes to make sure none of the vegetables are sticking to the bottom of the pot.
Once the chicken is cooked through, remove it to a plate and allow it to rest for a few minutes.
Shred the chicken and return it to the pot.
Stir in the wild rice, cover the pot, and simmer on medium low for 30 minutes, stirring every 5 minutes to prevent sticking.
Add the heavy cream and milk to the pot and stir.
Remove from the heat and serve immediately with a fresh slice of sourdough bread.