In a large stockpot, saute onions and garlic in olive oil until transparent. Stir in the chilies, cumin, and oregano. Cook and stir 2 to 3 minutes more.
Add broth, pork, and beans; bring to a boil. Reduce the heat to a simmer, and cook uncovered for 20 minutes.
Remove from heat, and stir in the cheese until melted.