In a medium bowl, whisk together the barbecue sauce ingredients.
7 ounces tomato paste, ¾ cup aged balsamic vinegar, 1 teaspoon Diamond Crystal kosher salt, ½ teaspoon black pepper, 1 teaspoon garlic powder, 1 teaspoon onion powder, 1 teaspoon smoked paprika, 2 tablespoons sweetener of choice
Pour the BBQ sauce over the meat. Use your hands to ensure the meat is well-coated.
Cover and cook on LOW for 8 hours or on HIGH for 5 hours.
Carefully remove the lid (hot steam will escape). Use two forks to shred the meat and mix it with the cooking juices.
Serve immediately.
Video
Notes
While it's important to use aged balsamic vinegar, stick with one with about 5 grams of sugar per tablespoon. Those with 10 grams of sugar per tablespoon are too sweet, at least to my palate.
Saltiness and sweetness preferences are highly personal. Adjust to taste.
For the best and most tender results, cook the meat on LOW for 8 hours. If you need to cook it for a shorter time, 5 hours on HIGH is acceptable. I tried cooking it on HIGH for 4 hours and it wasn't tender enough to shred, so I do recommend 5 hours.
When buying the meat, try to select a well-trimmed piece or ask the butcher to trim it for you. I've got nothing against fat (it's delicious!), but when making shredded meat, you don't want large pieces of fat in there.
You can keep the leftovers in an airtight container in the fridge for 3-4 days. Gently reheat them in the microwave at 50% power. Reheat them covered to prevent splatters and to prevent the meat from drying out.
You can also freeze the leftovers for up to three months. Thaw them overnight in the fridge and reheat them covered in the microwave.