Cut the chuck roast into large chunks (about 3").
Heat cooking fat in a large skillet over medium high. Add the chunks of beef and brown for a couple of minutes per side (don't worry about cooking through, just looking to add some color).
Transfer the meat to a slow cooker and add the remaining barbacoa ingredients (spices, lime juice, beef broth, garlic, and tomato sauce). Give it a stir and set the slow cooker to cook on "low" for 8 hours, or "high" for 6 hours.
Use two forks to shred the meat, reserving some of the liquid left behind.