Place a large pot or Dutch oven over medium heat and melt the butter. Add the onion, carrots, and celery. Sauté for about 5 to 7 minutes until the onions are translucent and the vegetables start to soften.

Stir in the minced garlic and cook for just 1 minute until you can smell the fragrance. Do not let the garlic burn.

Pour in the chicken broth and add the rinsed wild rice. Bring the mixture to a boil.

Once boiling, turn the heat down to low. Cover the pot with a lid and let it simmer for 45 to 50 minutes. The rice is done when the grains have softened and some have burst open.

While the rice cooks, prepare your chicken. If it is not already cooked, you can poach or pan-sear it, then shred it into bite-sized pieces.

Add the shredded chicken, thyme, rosemary, salt, and pepper to the pot once the rice is tender.

In a small bowl, whisk together the flour and the milk until the mixture is smooth and there are no lumps.

Slowly pour the milk mixture into the soup while stirring constantly. Continue to cook the soup over medium heat for another 5 to 10 minutes. The soup will thicken as it heats up.

Taste the soup and add more salt or pepper if needed. If the soup is too thick, you can add a splash more broth.

Remove from heat and serve warm.