Mix cumin, oregano, smoked paprika, salt, and pepper, together in a small bowl. Rub over all sides of the pork making sure to completely cover it.
Place the pork in the crock pot, fat side up.
Spread the minced garlic, green chilis, and onions over the top of the pork. Pour in the juice from the oranges and limes.
Cover crock pot and cook on low 10 hours or high 7 hours.
Remove the meat from the crock pot to a cutting board and shred with two forks.
Return the meat to the crock pot and let it simmer on low for 30 minutes. (If there seems to be a lot of juices, you can remove some of it first).
After simmering the meat, using tongs, transfer the meat to a large rimmed sheet pan. You may need more than one, make sure not to crowd it.
Place it under the broiler for 1-3 minutes. Watch it closely! You want some of the meat to brown up and become crispy, but not all of it.
Serve with soft shells, cilantro, diced avocado, guacamole, pico de gall, salsa etc.