Mix the rub: In a small bowl, combine salt, pepper, smoked paprika, garlic powder, onion powder, cumin, and chipotle powder.
Prep the pork: Pat the pork shoulder dry.
Rub it all over with oil, then coat evenly with the spice mix. Press the rub in so it sticks.
Make the cooking liquid: Whisk broth, apple cider vinegar, tomato paste, and Worcestershire. Add a few drops of liquid smoke if you like a BBQ note.
Choose your method: Slow cooker: Place pork in the crock, pour liquid around (not on top), cover, and cook on Low 8–10 hours or High 5–6 hours.
Instant Pot: Add liquid to the pot, place pork in, seal, and cook on High Pressure for 60–75 minutes (75 for larger roasts).
Natural release 15 minutes, then quick release.
Oven: Heat oven to 300°F (150°C). Put pork in a Dutch oven with the liquid, cover, and cook 3.5–4.5 hours until fork-tender.
Shred: Transfer the pork to a board and rest 10 minutes. Shred with two forks, discarding large fatty bits.
Reduce the juices: Skim excess fat from the cooking liquid.
Simmer the liquid for 5–10 minutes to concentrate. Toss the shredded pork with just enough reduced juices to keep it moist and flavorful.
Adjust and serve: Taste and season with extra salt, pepper, or a squeeze of lime. Garnish with cilantro if you like.
Serve in lettuce cups, low-carb tortillas, or over cauliflower rice.