Place the beef chuck roast in the slow cooker and add the sliced onion and minced garlic around it.
Pour the can of diced tomatoes with green chilies and the beef broth over the meat.
Sprinkle the chili powder, cumin, smoked paprika, salt, and black pepper evenly across the top.
Cover and cook on low for 8 hours until the beef shreds easily with two forks.
Shred the beef directly in the slow cooker and stir it into the juices to absorb flavor.
Warm the flour tortillas, then fill each one with a portion of the shredded beef, cooked rice, and shredded cheddar cheese.
Fold the sides of the tortilla inward and roll tightly to form each burrito.