Heat oil in a large pot over medium heat. Add onions and garlic; cook and stir until onions are tender, about 10 minutes.
Stir in chicken, broth, green chile peppers, cumin, oregano, and cayenne pepper; bring to a boil.
Reduce heat to low; add beans and simmer, stirring occasionally, until thoroughly heated, about 20 to 30 minutes.
Ladle soup into individual bowls and top with shredded cheese.