1. Heat the olive oil in a large heavy-bottomed pot or Dutch oven over medium heat. Add the diced onion, celery, carrots, and green bell pepper. Cook, stirring occasionally, until the vegetables are softened and beginning to brown at the edges, about 6 to 8 minutes.

2. Stir in the minced garlic and cook just until fragrant, about 30 seconds, being careful not to let it burn.

3. Add the shredded cooked chicken and pulled pork to the pot. Toss to combine with the vegetables and cook for 2 to 3 minutes to warm the meat through and let it pick up flavor.

4. Pour in the chicken broth, diced tomatoes with their juices, and tomato sauce. Stir in the barbecue sauce, Worcestershire sauce, and brown sugar. Add the bay leaf and stir, scraping up any browned bits from the bottom of the pot.

5. Add the diced potatoes and bring the mixture to a gentle boil. Once it reaches a boil, immediately reduce the heat to low, cover partially, and simmer for about 20 minutes, stirring occasionally, until the potatoes are nearly tender.

6. Stir in the frozen corn and lima beans. Season with smoked paprika, chili powder, cayenne pepper if using, kosher salt, and black pepper. Continue simmering uncovered for another 15 to 20 minutes, or until the vegetables are tender and the stew has thickened slightly.

7. Remove the bay leaf, then stir in the butter until melted for a silky finish. Taste and adjust seasoning with more salt, pepper, or barbecue sauce if desired.

8. Ladle the hot Brunswick stew into bowls, garnish with chopped fresh parsley, and serve with cornbread, biscuits, or crusty bread for dipping.