Season and sear the pork. Generously sprinkle salt and pepper over the entire surface of your pork shoulder, using your fingers to rub it into the pork. Meanwhile, add 1-2 tablespoons of olive oil to a large Dutch oven set over medium-high heat. Add the pork and sear on all sides, until lightly browned, but not charred.
Cook the onion. Remove the pork to a clean plate and set aside. Add four tablespoons of butter to the same pot set over medium heat and add the diced onions. Cook, stirring frequently, for 4-5 minutes or until starting to soften. Stir in the minced garlic and cook for an additional minute.
Add additional vegetables. Add the potatoes, corn, lima beans, diced tomatoes, and chicken broth. Thoroughly mix to combine. Return the pork back to the pot, nestling under the mixed vegetables so that it is completely submerged in broth.
Cook. Bring to a low boil before reducing heat to a simmer. Cover and allow pork to simmer for at least 2-3 hours.
Remove pork and shred. Remove the pork shoulder from the pot and set aside until cool enough to handle. Use two large forks (or your hands) and shred into chunks. Once all the pork has been shredded, return the pork AND the bone back to the pot (the bone still has flavor).
Season. Add the barbecue sauce, brown sugar, Worcestershire sauce, salt, black pepper, and cayenne pepper (if using) and mix well to combine. Season with additional salt and pepper, to taste. Continue to simmer, uncovered, for an additional 15 minutes.
Serve with your favorite cornbread recipe and coleslaw for a complete meal. Enjoy!