Preheat the oven to 300 degrees. In a large bowl, toss the pork pieces, paprika, chili powder, cumin, granulated garlic, onion powder, ground mustard, oregano, salt, and pepper, until well combined.
In a 6 quart dutch oven, heat the avocado oil over medium high heat. Working in batches, sear 2-3 pieces of pork at a time for about a minute on all sides until brown.
Remove the seared pork from the pot and set aside.
Turn the heat down to medium and add the onions. Sauté for 5 minutes.
Deglaze the pot with the apple cider vinegar, scraping any brown bits off the bottom.
Stir in the soda, barbecue sauce, and worcestershire sauce.
Add the pork back in so it is mostly covered in the liquid. Bring to a boil.
Cover and transfer to the oven.
Bake for 3 hours.
Remove the pork from the pot and place in a large shallow bowl. Using two forks, shred the pork. Transfer the shredded pork back into the dutch oven with its juices.