1. Heat 1 tablespoon oil in a large skillet over Medium-High. Add pork pieces and cook 6 to 7 minutes until browned, turning occasionally.
2. Place browned pork, chicken broth and green chiles in a 4- to 5-quart slow cooker. Cover and cook on High for 4 1/2 hours (Low: 9 hours). Remove pork only (leaving chiles in the pot) and set aside; keep warm.
3. Stir rice into the liquid in slow cooker. Cover and cook on High for 10 minutes or until moisture is absorbed and rice is tender. Stir in remaining 2 tablespoons olive oil and 1/4 cup cilantro. Place in a shallow serving bowl or pasta bowl, top with cheese.
4. Roughly pull pork apart, leaving in large chunks and place on top of cheese, sprinkle with remaining cilantro and serve with lime wedges.