I make this when I know my day at work will be really long, and I won't want to cook when I get home. My daughter likes this meat when I roll it in a soft taco size tortilla and fry it as a flauta. The ends of the meat get caramelized when you do that.
Peel the garlic. Cut slits in the roast and insert the garlic cloves. Put the meat in the slow cooker and season with salt, pepper, cumin and chipotle chili powder to taste. Chop the onion and add to the slow cooker, along with the green chilies and the beef broth.
Cook on low for about 8 hours.
Shred the meat using a couple of forks. I like my meat lean, so I discard the fat. Ladle some of the cooking broth over the meat; this helps keep it moist.
Note: We use this meat for burritos, chimichangas, flautas and tacos. It is really good with "the works" - like salsa, guacamole, lettuce, tomato, cheese and sour cream.