In a large pot, heat oil over medium heat. Add onion and pepper and cook until translucent, 6-7 minutes. Add garlic and cook an additional minute, until fragrant.

Dissolve the cornstarch in the chicken broth then add it to the pot. Add the chicken, chopped tortillas, lime juice, diced tomatoes, green chiles, cumin, cayenne, oregano, and salt.

Increase the heat to medium high. When the soup begins to bubble, reduce the heat to low and allow to simmer for about 20 minutes, stirring occasionally, until tortillas are very soft and mostly melted into the soup.

Lower the heat to medium low and add cheese. Stir continuously, running the spatula along the bottom and sides of the pan, until the cheese is melted into the soup. Be sure to run your spatula along the bottom of the pan occasionally to ensure the cheese isn't sticking to the bottom. Serve with crunchy tortilla chips and chopped cilantro.