Place the beef chuck roast in the slow cooker. Add the sliced onion and minced garlic on top.
In a small bowl, stir together the chili powder, cumin, salt, and black pepper. Rub the spice mixture evenly over the beef.
Pour the beef broth and salsa around the sides of the roast so the spices stay on top.
Cover and cook on low for 8 hours or until the beef shreds easily with two forks.
Shred the beef directly in the slow cooker, then stir in the drained black beans. Let everything warm together for 10 minutes.
Spoon the shredded beef mixture over the cooked brown rice in bowls. Add shredded cheddar cheese, diced avocado, chopped cilantro, and lime wedges to finish.