In a large pot or Dutch oven, melt the butter over medium heat. Add the finely chopped onion and sauté until it's translucent, about 5 minutes.

Add the minced garlic and cook for another minute until it becomes fragrant.

Stir in the tomato paste, ensuring it mixes well with the onions and garlic. Cook for about 2 minutes to enhance its flavor.

Pour in the chicken or beef broth and bring the mixture to a gentle simmer.

Add the diced tomatoes, frozen corn, lima beans, BBQ sauce, brown sugar, Worcestershire sauce, salt, black pepper, dried thyme, smoked paprika, and cayenne pepper. Stir everything together to combine.

Gently fold in the BBQ pulled pork, pulled beef, and shredded chicken, ensuring the meats are evenly distributed throughout the stew.

Cover the pot and let the stew simmer on low heat for about 45 minutes to 1 hour, stirring occasionally. This allows the flavors to meld.

Taste the stew and adjust the seasonings if needed, adding more salt, pepper, or cayenne pepper to suit your preference.

Serve with cornbread or crusty bread and enjoy!