Generously salt and pepper chunks of meat on all sides.
In a large dutch oven, heat oil over medium-high heat. Once hot, add meat to the pan and brown on all sides. You may need to do this in batches, and it will take 10 to 15 minutes.
Transfer meat and any juices to your slow cooker and return pan to the stove. Add a splash of the chicken broth and deglaze the pan over medium-high heat, using a wooden spoon or spatula to scrape all the crispy browned bits off the bottom of the pan. Pour everything over the top of the meat in the slow cooker.
To the slow cooker, add onions, garlic, lime juice, spices, and enough chicken broth to just cover the top of the meat. Cook on high for 3 to 4 hours or low for 7 to 8. The meat is ready when it can be easily shredded with a fork.
Preheat the oven to 400°F. Transfer the meat, a few pieces at a time, to a plate and shred. Place shredded meat on a baking sheet and sprinkle with salt. If you had a large roast, you may need to split the meat between two baking sheets. Pour ¼ cup of the cooking liquid over the top of the meat. Bake until crispy, about 30 minutes, checking every 10 minutes and adding more cooking liquid if meat seems to be drying out.
Or broil meat on high for 5 to 10 minutes until crispy, checking on frequently. DO NOT leave broiling meat unattended as it can burn very quickly.