Step 1: Season the beef chuck roast generously with salt and freshly ground black pepper on all sides.
Step 2: Heat the olive oil in a large skillet over medium-high heat. Sear the beef chunks in batches until browned on all sides. This step is crucial for developing deep flavor. Transfer the browned beef to the slow cooker.
Step 3: Add the chopped onion to the same skillet and cook until softened, about 5 minutes. Stir in the minced garlic and cook for another minute until fragrant.
Step 4: Deglaze the pan with a splash of beef broth, scraping up any browned bits from the bottom. Pour the onion and garlic mixture over the beef in the slow cooker.
Step 5: Add the diced tomatoes, green chilies, remaining beef broth, chili powder, ground cumin, dried oregano, smoked paprika, and cayenne pepper (if using) to the slow cooker. Stir gently to combine. Add the bay leaf.
Step 6: Cover the slow cooker and cook on low for 6-8 hours, or on high for 3-4 hours, or until the beef is fork-tender and easily shreds.
Step 7: Once cooked, carefully remove the beef from the slow cooker and place it on a large cutting board. Using two forks, shred the beef. Discard the bay leaf.
Step 8: Return the shredded beef to the slow cooker, stirring it back into the flavorful cooking liquid. Taste and adjust seasonings as needed.
Step 9: Serve warm with fresh cilantro and lime wedges, alongside your favorite Mexican accompaniments like tortillas, rice, beans, or over salads.