Heat large soup pot or Dutch oven over medium heat and add olive oil. Once olive oil is sizzling, add onions, bell peppers, garlic and sauté until onions and peppers are tender.
Make space in the middle of pot and add oregano, chili powder, paprika, and cumin. Combine seasoning and keep it from burning. Once seasoning is combined, mix with onion mixture.
Next stir in roasted hatch chiles, pork, wine and mix well. Place cover on the pot or Dutch oven, turn heat to low and simmer for 25-30 minutes.
Garnish with cilantro and/or shredded white cheddar and serve with lime wedges.