Arrange the bacon on a rimmed baking sheet. Sprinkle with the brown sugar and cracked pepper. Bake until the bacon is crisp and the sugar is gooey, 15 to 18 minutes. Remove from the oven, keep warm and set aside. Leave the oven on.
While the bacon bakes, heat a cast-iron griddle over medium heat until hot.
Spread the mayonnaise on the split sides of the buns and griddle mayo-side down until golden brown, 1 to 2 minutes. Set aside.
Shape the beef into 4 equal patties. Spread the mustard over each patty and season with salt and pepper.
Heat a large cast-iron skillet over medium-high heat. Add the patties and cook for 4 to 5 minutes. Add the butter and flip the patties.
Top the patties with the blue cheese crumbles. Bake until the cheese starts to yield--the blue cheese will not melt--2 to 3 minutes.
Meanwhile, spread the steak sauce on the bottom buns. Top with the patties and bacon. Close the burgers and serve hot.