Heat the olive oil in a large pot over medium heat. Add the pork cubes and cook until browned on all sides, about 6 minutes. Remove the pork and set it aside.
Add the onion to the same pot and cook until softened, about 4 minutes. Stir in the garlic and cook for 1 minute more.
Return the pork to the pot. Pour in the crushed tomatoes and chicken broth. Add the minced chipotle peppers, cumin, and oregano. Season with salt and black pepper.
Bring the mixture to a simmer, then reduce the heat to low. Cover and cook for 45 minutes, stirring occasionally, until the pork is tender.
Stir in the black beans and simmer uncovered for 10 more minutes to heat them through and thicken the broth slightly.
Ladle the stew into bowls and top with chopped cilantro. Serve with lime wedges on the side.