Trim and prep the pork: Pat the pork shoulder dry. Trim any large, hard pieces of external fat, but leave a decent layer for moisture.
Mix the dry rub: In a small bowl, combine 2 tsp salt, 1 tsp pepper, 2 tsp smoked paprika, 1 tsp garlic powder, 1 tsp onion powder, 1 tsp cumin, 1–2 tsp chili powder, and a pinch of cayenne if you like heat.
Season generously: Rub the pork all over with 1–2 tbsp oil, then coat with the spice mix, pressing it into all sides.
Choose your cooking method: Slow cooker on Low for 8–10 hours (or High for 5–6), oven at 300°F (150°C) for 3.5–4.5 hours in a covered Dutch oven, or pressure cooker for 60–75 minutes with natural release.
Add 1/2 cup broth and 2 tbsp apple cider vinegar to the pot, regardless of method.
Make the keto BBQ sauce: In a saucepan, whisk 1 cup sugar-free ketchup, 2–3 tbsp brown sugar substitute, 2 tbsp apple cider vinegar, 1 tbsp Worcestershire sauce, 1 tsp Dijon, 1/2 tsp smoked paprika, and a few drops of liquid smoke. Simmer 5–7 minutes until slightly thick. Adjust sweetness, tang, and heat to taste.
Set aside.
Check for doneness: The pork is ready when it shreds easily with forks. If it resists, cook a little longer.
Shred and moisten: Transfer pork to a tray and shred with two forks, discarding large fat pieces. Skim excess fat from the cooking liquid.
Toss the shredded meat with some of the strained juices and 1/2–3/4 cup BBQ sauce until juicy but not soupy.
Optional finishing touch: Stir in 1 tbsp butter for a glossy finish and extra richness.
Prep low-carb sides: Quick slaw: Toss coleslaw mix with mayo, a splash of vinegar or lemon, salt, pepper, and a pinch of celery seed.
Cauliflower mash: Steam florets until tender, then blend with butter, a splash of broth, salt, and pepper.
Green beans: Sauté in olive oil with garlic until crisp-tender; season well.
Portion for meal prep: Divide pork and sides into containers. Drizzle a bit of extra sauce over the pork and save the rest to add after reheating.