Sauté the Vegetables: In a large Dutch oven or stockpot, melt the butter over medium heat. Add the diced onion, carrots, and celery and cook until softened, about 5-7 minutes. Stir in the minced garlic and cook for another minute until fragrant.

Make the Roux: Sprinkle the flour over the vegetables and stir constantly for one minute. This cooks out the raw flour taste and is the essential step for thickening the soup.

Simmer the Soup: Slowly whisk in the chicken broth, a little at a time, to prevent lumps. Add the wild rice blend, chicken breasts, thyme, rosemary, salt, and pepper. Bring the mixture to a boil, then reduce the heat to low, cover, and let it simmer for 40-45 minutes, or until the rice is tender and the chicken is cooked through.

Shred the Chicken: Carefully remove the cooked chicken breasts from the pot and place them on a cutting board. Use two forks to shred the meat into bite-sized pieces, then return it to the soup.

Add the Cream: Stir in the heavy cream and let the soup warm through for another 5 minutes. Be careful not to let it boil after adding the cream. Taste and adjust seasoning if necessary. Serve hot.