Place the beef chuck roast in the slow cooker. Add the diced onion, minced garlic, black beans, and diced tomatoes with green chilies.
Pour in the beef broth. Sprinkle the chili powder, cumin, oregano, salt, and black pepper over the top.
Cover and cook on low for 8 hours until the beef is very tender.
Remove the beef to a cutting board and shred it with two forks. Return the shredded beef to the slow cooker and stir everything together.
Ladle the soup into bowls and top with cilantro, a squeeze of lime, and shredded cheddar cheese.