Heat the oil in a large pot over medium heat. Add the pork pieces and brown them on all sides, about 6 to 8 minutes total.
Add the onion and cook for 3 minutes until it starts to soften. Stir in the garlic and cook for 1 minute more.
Add the chipotle peppers, cumin, and oregano. Stir everything together and cook for 1 minute to release the flavors.
Pour in the chicken broth and bring the mixture to a simmer. Scrape the bottom of the pot to loosen any browned bits.
Add the potatoes and carrots. Reduce the heat to low, cover the pot, and simmer for 45 to 55 minutes until the pork and vegetables are tender.
Taste and season with salt and black pepper. Ladle the stew into bowls and top with chopped cilantro. Serve with lime wedges on the side.