
Heat 1 tablespoon oil in a large pot over medium heat. Add 1 cup onion and cook, stirring occasionally, until softened, about 3 minutes. Add 3 cloves garlic and cook, stirring, for 1 minute. Add 5 cups broth, 1 can diced tomatoes, 1 can chiles, 6 corn tortillas, 2 teaspoons chili powder and 1 teaspoon cumin. Bring to a boil, stirring occasionally. Reduce heat to a simmer. Cover and cook for 20 minutes.
Add 2 cups shredded chicken and 4 ounces cream cheese, stirring until the cream cheese is melted. Remove from heat. Combine ¾ cup shredded cheese and 1 ½ teaspoons cornstarch in a small bowl and gradually add to the soup, stirring until melted. Return the pot to medium heat and cook until hot, 1 to 2 minutes. Serve the soup with cilantro, sour cream and/or guacamole, if desired.