Heat a large skillet over medium-high heat. Cook and stir pork in the hot skillet until browned and crumbly, 5 to 7 minutes. Drain and discard grease.

Heat oil in a large stockpot over medium heat. Add onions and garlic; sauté until onions are transparent, about 5 minutes. Stir in chiles, cumin, and oregano; cook and stir until fragrant, 2 to 3 minutes. Add broth, cooked pork, and beans; bring to a boil. Reduce the heat and simmer, uncovered, for 20 minutes.

Remove from the heat and stir in Monterey Jack until melted.