Season pork cubes with salt and pepper. Heat oil in large Dutch oven and sauté pork in batches until nicely browned on all sides, about 5 minutes. Transfer pork to a plate. Stir in onion, chiles and garlic and cook, stirring for 2 to 3 minutes, until onion is soft. Add pork back in along with broth, cilantro, zest and juice. Bring to a boil. Simmer uncovered, stirring occasionally, for about 1 1/4 hours, until meat is fork-tender and liquid has thickened.
Serve garnished with lime wedges and chopped cilantro with warm tortillas and black beans on the side.
Serving Suggestion: In Mexico, pork is often cooked with lime and served with more lime. This very flavorful, stew-like dish can be served with hominy, rice, or potatoes. You can also add black beans and corn. Also can be served as part of Pastel de Cerdo y Limon.