Heat the oil in a large soup pot or Dutch oven over medium heat. Add the onion, carrots, and celery, then cook for about 5 minutes, stirring occasionally, until the vegetables begin to soften.

Stir in the minced garlic and cook for 30–60 seconds, just until fragrant. Keep the heat moderate so the garlic does not brown or turn bitter.

Sprinkle in the flour, salt, dried parsley, and black pepper. Stir continuously for about 1 minute so the flour coats the vegetables and loses its raw taste.

Gradually whisk in the low-sodium chicken broth, scraping the bottom of the pot to loosen any flour. Continue whisking until the broth is smooth and the mixture begins to come together.

Stir in the uncooked wild rice and bring the soup to a boil. Reduce the heat, cover the pot, and simmer for about 35–45 minutes, or until the rice is tender.

Check the wild rice before proceeding because cooking times vary by blend. If the rice is still firm, continue simmering until tender before adding the milk and chicken.

During the final 5–10 minutes, stir in the evaporated milk or 2% milk and the cooked, shredded chicken. Heat gently until the chicken is hot and the soup is creamy, avoiding a prolonged hard boil.

Taste the finished soup and adjust the salt and black pepper as needed. Ladle into bowls and serve hot with a little dried parsley or your favorite simple side.