Heat the oven to 300°F (150°C). Cover the ancho chiles with hot water and soak for 15 minutes. Drain; discard the soaking water. Let the chiles cool enough for safe blending, then blend with the onion, garlic, chipotle, cumin, oregano, vinegar and broth until smooth. Follow your blender's precautions for warm liquids; never seal boiling liquid in a closed blender.

Pat the beef dry and season with the salt. Heat the oil in the Dutch oven over medium-high heat. Brown the beef in batches on several sides, about 8–10 minutes total, without crowding.

Return all beef to the pot and pour in the chile sauce. Bring just to a simmer, cover tightly and transfer to the oven.

Braise for about 3–3 1/2 hours, checking after 2 1/2 hours. Add a little water if the sauce is drying out. The beef is ready when a fork separates it easily; if still firm, cover and continue in 20-minute intervals. Timing depends on the cut and chunk size.

Rest covered for 10 minutes, then move the beef to a plate and shred with two forks. Skim excess fat from the sauce. If the sauce is thin, simmer it uncovered briefly on the stove before returning the beef. Stir in the lime juice and enough sauce to coat the shreds; divide into six servings.