Heat the oil in a large skillet over medium-high heat. Once it’s nice and hot, sear the beef in batches, browning it on all sides. Transfer the seared meat to your Crockpot.
Scatter the onions and garlic over the top.
In a bowl, whisk together the beef broth, green chiles, chipotle chiles with adobo, lime juice, salt, pepper, Mexican oregano, cumin, chili powder, and ground cloves. Pour the sauce over the beef, then add the bay leaves.
Cover and cook on low for 6–8 hours or high for 3–4 hours, until the beef is super tender and falls apart easily.
About 30 minutes before it’s done, remove the beef and shred it using two forks.
Return the shredded beef to the Crockpot and stir it into the sauce. Cover again and let it finish cooking so it can soak up all that flavor. Remove and discard the bay leaves before serving.
Sprinkle with fresh cilantro and serve with extra lime wedges on the side.