Prepare the Chiles:
Heat a small skillet over medium heat and toast the dried ancho and guajillo chiles for about 2 minutes, until fragrant.
Remove the chiles from the skillet and place them in a bowl of hot water. Let them soak for 10-15 minutes, or until softened.
Sear the Beef:
While the chiles are soaking, season the beef chuck roast with salt and pepper.
Heat olive oil in a large skillet over medium-high heat. Sear the beef on all sides until browned, about 4-5 minutes per side. Transfer the beef to the slow cooker.
Blend the Sauce:
After the chiles have softened, transfer them to a blender or food processor. Add the garlic, onion, vinegar, cumin, oregano, coriander, paprika, cinnamon, lime juice, and beef broth.
Blend until smooth, then pour the sauce over the beef in the slow cooker.
Slow Cook the Beef:
Cover the slow cooker and cook on low for 8-10 hours, or until the beef is fork-tender and easily shreds.
Shred the Beef:
Remove the beef from the slow cooker and use two forks to shred the meat. Discard any large fat pieces.
Serve:
Return the shredded beef to the slow cooker and mix it into the sauce. Let it simmer for another 15-20 minutes to absorb the flavors.
Serve the barbacoa in tacos, burritos, or over rice, and garnish with fresh cilantro and lime wedges.