Sear the beef chunks: Pat the 3-inch chunks of chuck roast completely dry with paper towels. Season all sides generously with kosher salt and black pepper. Heat 2 tablespoons of oil in a large heavy skillet or Dutch oven over high heat. Sear the beef chunks in batches for 2 to 3 minutes per side until deeply browned and caramelized. Transfer the seared beef directly into the slow cooker basin.
Blend the smoky adobo sauce: In a blender or food processor, combine the chipotle chiles in adobo, beef bone broth, garlic cloves, chopped onion, apple cider vinegar, fresh lime juice, ground cumin, dried Mexican oregano, ground cloves, and salt. Puree on high speed for 45 to 60 seconds until completely smooth and velvety.
Pour and slow cook: Pour the pureed adobo sauce evenly over the seared beef chunks in the slow cooker. Tuck the 3 bay leaves deep into the liquid between the meat. Cover with the slow cooker lid and cook on LOW for 8 to 9 hours (or on HIGH for 4.5 to 5 hours) until the beef is fork-tender and shreds effortlessly with zero resistance.
Shred the barbacoa: Remove the bay leaves and discard. Using two forks, shred the beef chunks into juicy, succulent shreds directly in the slow cooker basin so they drink up the bubbling, rich braising liquid.
Soak and adjust seasoning: Toss the shredded beef in the warm sauce and let it rest on the 'WARM' setting for 10 to 15 minutes to fully absorb the seasonings. Taste and add an extra pinch of sea salt or squeeze of fresh lime juice if desired.
Serve street-style: Spoon generous mounds of juicy barbacoa into warm double corn tortillas. Top with fresh diced white onion, chopped cilantro, crumbled cotija cheese, and a squeeze of fresh lime juice. Serve hot with guacamole, black beans, or cilantro lime rice!