Combine meat with breadcrumbs, egg, hot sauce, salt & pepper. Mix well, and form into eight patties of the same size.
Divide the blue cheese into four equal portions. Place a portion of the cheese atop one patty, then top with another patty. Fold the patty's edges together so the cheese is hidden in the center. Seal well so nothing leaks out when cooking. Repeat three more times to make four burgers in total.
Heat the butter in a skillet of medium-high heat. Cook patties, flipping once, for about 15 minutes.
Serve inside buns and top with more hot sauce, if desired. Maybe some sliced red onions, tomato and lettuce as well. I served mine in pitas and topped with baby arugula and hot sauce.