Mix the BBQ Pulled Pork with the BBQ Sauce and heat in a small pan over medium heat, ensuring not to burn.
To prepare the patties, sprinkle the ground beef with 1 tablespoon salt and 1 tablespoon pepper. Mix well. Divide the beef into 4 burgers to create 5-inch-wide, even burgers. Do not over mix or squish, because this will cause the burgers to be tough.
To cook the burgers, ladle the bacon fat on a hot flat top grill or in a saute pan over medium-high heat. Once the bacon fat is hot, add the burgers and cook for 4 minutes on the first side, and then flip and repeat the cooking. This should yield a medium burger. For higher cook temperature, finish in a 400 degree F oven to desired temperature. Once cooked to desired temperature, top with the BBQ pork and a slice of cheese. Allow to melt for 1 minute.
During this time, spread the butter on the buns. Then place the buttered side on the flat top or in the pan to brown the butter; this will create "sealed" bread to build the burger on.
Begin assembling the burger. Take the buns off the grill and place 1/4 cup slaw on each cooked bottom bun, then a tomato slice, 2 red onions and the burger patty. Finish with the top bun. A skewer can be placed to hold the burger together.
To prepare the pork, preheat the oven to 275 degrees F. Then sprinkle the pork with the Cajun spice and place in a 6-inch-deep casserole or roasting dish. Next, add the stock, vinegar and vegetables. Cover with foil and place in the oven for 3 hours. Once cooked, remove the pork and allow to cool. Then pick or shred the meat.
In a bowl, whisk together the ketchup, mustard, Worcestershire sauce, sugar, vinegar and spice. Then, in a small saucepan over low heat, cook for 10 to 12 minutes to blend the flavors, stirring throughout. Once cooked, remove from the heat and hold. The BBQ sauce yields 2 cups.