Sauté the Aromatics: Heat the oil in a large pot or Dutch oven over medium heat. Add the diced onion and minced garlic. Sauté for 3-4 minutes until the onion softens and the garlic is fragrant.
Add beans and tomato paste: Stir in the raw lima beans and tomato paste. Cook for 2-3 minutes, stirring frequently, to coat the beans in the tomato paste.
Incorporate proteins and spices: Add the shredded chicken and pulled pork to the pot. Sprinkle with smoked paprika, cayenne pepper, salt, and black pepper. Continue to sauté for 5 minutes, stirring to evenly distribute the spices and slightly caramelize the meat.
Add remaining ingredients: Pour in the chicken broth and stir well to deglaze the pot. Add the barbecue sauce, Splenda, corn, and Worcestershire sauce. Mix thoroughly, ensuring all ingredients are evenly combined.
Simmer: Bring the stew to a gentle boil, then reduce the heat to low. Cover the pot and let it simmer for 45 minutes, stirring occasionally. This allows the beans to cook through.
Thicken the stew: Uncover the pot and simmer for an additional 20-30 minutes, stirring occasionally. If the stew thickens too much, add a little more chicken broth to adjust the consistency to your liking.
Serve: Ladle the Brunswick Stew into bowls and serve hot. Pair it with crusty bread or a simple side salad.