Season the pork cubes generously with salt and pepper. Heat the oil in a large Dutch oven over medium-high heat.
Working in batches, brown the pork on all sides, about 8 minutes total. Remove and set aside.
In the same pot, sauté the onion until softened, about 5 minutes. Add garlic and cook for 1 minute until fragrant.
Stir in the chipotle peppers, adobo sauce, cumin, chili powder, and oregano. Cook for 1 minute to toast the spices.
Return the pork to the pot and add the chicken broth and diced tomatoes. Bring to a boil, then reduce heat to low.
Cover and simmer for 1.5 hours, stirring occasionally, until the pork is tender.
Add the potatoes and carrots, then continue cooking uncovered for 45 minutes until vegetables are tender.
Taste and adjust seasoning. Serve hot, garnished with fresh cilantro and lime wedges. Even better reheated the next day!