Combine salt, pepper, cumin, oregano, paprika, and chili powder in a bowl.
Pat pork dry and cut into 3–4 chunks.
Rub pork with the spice blend and minced garlic.
Heat olive oil in a skillet and brown the pork on all sides.
Spread the sliced onion in the bottom of the slow cooker.
Set the browned pork on top of the onions.
Whisk orange juice, lime juice, broth, chipotle, and brown sugar.
Pour the mixture around the pork, not directly on top.
Cook on LOW until fork-tender, about 8 hours.
Transfer pork to a pan and shred with two forks.
Skim fat from the cooking liquid and simmer to reduce for 8 minutes.
Toss the shredded pork with the reduced juices.
Broil on a sheet pan to crisp edges, 4–5 minutes, if desired.