In a large pot, heat the oil over medium-high heat. Add the vegetables and garlic and sauté for 5 minutes. Add the broth and bring to a boil. Reduce the heat to medium-low and simmer, covered, for about 10 minutes. Stir in the chiles.
In a medium bowl, whisk together the milk, flour, salt, chili powder and cumin. Increase the heat to high and whisk the milk mixture into the soup. Stir until slightly thickened and bubbly, about five minutes. Reduce the heat to low. Add the turkey, cheese, corn and cilantro; stir until the cheese is melted and the soup is hot, 5 to 10 minutes.
*If preparing this recipe as gluten-free, substitute another thickener in place of the all-purpose flour- cornstarch or tapioca flour work well.
*You could certainly substitute shredded chicken for the turkey to make Mexican Chicken Soup.