Season and sear the beef: Pat the beef dry and season with salt and pepper. Heat oil in a large skillet over medium-high. Sear the beef on all sides until browned, 2–3 minutes per side.
Transfer to a slow cooker.
Build the sauce: In the same skillet, add onion and cook 2 minutes until slightly softened. Stir in garlic for 30 seconds. Add chipotles, adobo sauce, cumin, oregano, coriander, and cloves.
Cook 1 minute to bloom the spices.
Deglaze: Pour in the beef broth, scraping up browned bits. Stir in lime juice and apple cider vinegar. Pour everything over the beef in the slow cooker.
Nestle in the bay leaves.
Slow cook: Cover and cook on Low for 8–9 hours or High for 4–5 hours, until the beef shreds easily with two forks.
Shred and reduce: Remove the beef and shred. Skim excess fat from the cooking liquid, then simmer the liquid in a saucepan 5–10 minutes to slightly reduce, or leave it as is for juicier meat.
Combine and taste: Return shredded beef to the slow cooker with some of the reduced liquid. Taste and adjust salt, lime, and heat.
Add more adobo or a pinch of salt if needed.
Warm tortillas: Heat tortillas in a dry skillet or directly over a low flame until soft and pliable. Wrap in a towel to keep warm.
Assemble tacos: Fill tortillas with barbacoa. Top with onion, cilantro, and a squeeze of lime.
Serve with extra sauce on the side.