How to Make It
Heat 2 tablespoons of the oil in a Dutch oven over medium-high. Add pork, and cook, stirring until crumbled and no longer pink, 6 to 8 minutes. Drain pork, and set aside. Wipe Dutch oven clean.
Heat remaining 2 tablespoons oil in Dutch oven over medium. Add onion, poblano, garlic, green chiles, cumin, and salt, and cook, stirring often, until vegetables are tender, 3 to 4 minutes.
Increase heat to high. Stir in beans, broth, and pork, and bring to a boil. Reduce heat to medium-low, and simmer, stirring occasionally, until heated through, about 40 minutes. Add cheese and lime juice, and stir until cheese is melted. Serve immediately.