In a medium bowl, whisk together the barbecue sauce ingredients (tomato paste, balsamic vinegar, smoked salt, black pepper, garlic powder, smoked paprika, and sweetener).
Pour the BBQ sauce over the pork and use your hands to make sure the pork is well-coated.
Cover and cook on LOW for 8 hours.
Carefully remove the lid (hot steam will escape). Increase the heat to HIGH. Use two forks to shred the meat and mix it well with the sauce (remove the butcher twine if needed).
Cover and cook until slightly thickened, 15-30 more minutes, then serve.
Video
Notes
If you have a choice between pork shoulder (the lower part of the shoulder) and pork butt (the upper part), go with pork butt, aka Boston butt. It's tasty and fatty and won't dry out during the slow cooking process. Pork shoulder is best when making a pork roast.
I don't recommend using pork loin. It's too lean and will produce drier, inferior results.
I'm not usually a fan of buying specialty ingredients. But in this recipe, I find that smoked salt greatly enhances the flavor of the BBQ sauce and of the entire dish. So it's highly recommended.
If using store-bought BBQ sauce, you will need 1.5 cups.
As with most slow-cooked meats, the leftovers are great. You can keep them in an airtight container in the fridge for 3-4 days. They taste great even on the last day, and in fact, they improve as the flavors meld. To prevent them from over-drying, reheat them covered in the microwave.
You can also freeze the cooled leftovers for up to three months. Thaw them overnight in the fridge before reheating.