In a medium pan, fry both sides of bread slices in bacon fat. Remove from heat and lay out both slices of bread; place a slice of cheddar on each side.
Smother pork shoulder in barbecue sauce and heat until sauce is caramelized. Place pork on top of cheddar.
Place bacon on top of pork, then add provolone. Close sandwich and grill over medium heat, about 1 minute per side, until cheese is melted.