In a large stock pot over medium heat, add the roasted chicken, pulled pork, lima beans, corn kernels, potatoes, and broth.
Stir the ingredients together until all of the ingredients are combined.
Add in the canned tomatoes, barbecue sauce, brown sugar, Worcestershire sauce, garlic cloves, black pepper, cayenne pepper, and bay leaves. Stir to combine.
Bring the mixture to a boil, then reduce the heat to low and simmer for 20 minutes.
After 20 minutes, add in the early peas and butter. Stir to combine and cook until the peas are tender and the stew has thickened about 10 more minutes.
Serve hot with cornbread and coleslaw on the side.