Let the pork shoulder sit at room temperature for about 30 minutes. Preheat your oven to 300°F.

Use a large chopping knife to cut the shoulder into 3-4 large chunks.

Liberally season the cut pieces of pork with BBQ seasoning. Rub the dry seasoning into all sides of the pork shoulder, making sure to get seasoning into every nook and cranny. 

Combine the beef broth, apple cider vinegar, BBQ sauce, and mustard in a small bowl to make the braising liquid. Whisk until fully combined and then set aside. 

Heat the olive oil in the bottom of a cast iron, enameled Dutch oven over medium heat.

Working in batches, brown all sides of the cut pieces of pork. Sear the meat for about 2 minutes per side. Adjust the heat as necessary. You want your oil to stay hot but not burn and smoke.

Remove all pieces of browned meat from the Dutch oven and add the sliced onion. Saute the onion for about 3 minutes, until soft and fragrant. 

Add the pork back to the Dutch oven with the cooked onions. Pour the braising liquid over top of the pork. Bring the liquid up to a simmer.  

Cover the Dutch oven with the Dutch oven's tight-fitting lid, and transfer it to your preheated oven. Let the pork cook for 3 hours. 

After 3 hours, remove the pork from the oven. It should be fork-tender and easily pull apart. Use a large slotted spoon or kitchen tongs to transfer the pork pieces to a large mixing bowl. Shred the pork using two forks or meat claws. Remove any bone pieces while you're shredding. 

Use a slotted spoon to remove the sliced onion from the Dutch oven and mix it into the pulled pork. 

Mix in pan juices to taste. The cooking liquid remaining in the Dutch oven will keep the pork moist and juicy. Add anywhere from ½ cup and up. 

Serve Dutch Oven Pulled Pork with extra BBQ sauce drizzled on top. Enjoy!