In a large pot or Dutch oven, heat the olive oil over medium-high heat. Add the pork pieces and brown on all sides, about 5-7 minutes. Remove the pork and set aside.

In the same pot, add the diced onion and cook until softened, about 3-4 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.

Return the browned pork to the pot. Add the diced tomatoes, black beans, chopped chipotle peppers, cumin, smoked paprika, oregano, salt, and pepper. Pour in the chicken broth and stir to combine.

Bring the mixture to a simmer, then reduce the heat to low. Cover and cook for 1.5 to 2 hours, or until the pork is tender and easily shredded with a fork. Stir occasionally and add more broth if needed.

Once cooked, shred the pork in the pot using two forks and mix well with the beans and sauce. Adjust seasoning if necessary.

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