In a large pot or Dutch oven, heat the olive oil over medium-high heat.

Add the pork shoulder and brown on all sides, about 5-7 minutes.

Remove the pork from the pot and set aside. In the same pot, add the diced onion and cook until softened, about 5 minutes.

Stir in the minced garlic and cook for another minute until fragrant.

Add the diced green chili peppers and cook for 3-4 minutes until they start to soften.

Return the browned pork to the pot, then add the diced tomatoes, chicken broth, ground cumin, smoked paprika, salt, and pepper.

Bring the mixture to a boil, then reduce the heat to low and cover the pot.

Simmer the stew for about 1.5 to 2 hours, or until the pork is tender and the flavors have melded together.

Once done, taste and adjust seasoning if necessary.

Serve hot, garnished with fresh cilantro and lime wedges on the side.