To prepare the sauce, mix together mayonnaise, relish, ketchup, and BBQ sauce. Set aside.
Heat the griddle to medium-low and add oil and butter. Toss the diced onions to coat them evenly and cook until translucent. Add the brown sugar and a sprinkle of Bootleg Burger Seasoning, stirring to combine. Continue cooking until the onions are caramelized, then remove them from the griddle. On another part of the griddle, cook the bacon to your preferred crispness, then remove and set aside.
Season the ground beef with Bootleg Burger Seasoning and divide it into four equal portions. Loosely shape each portion into a ball. Turn the griddle heat to medium-high and place the balls of meat onto the griddle. Use parchment paper and a burger smasher to press each ball into a thin patty, holding the press for ten seconds. Spread a thin layer of mustard onto the patties and cook them for about 1.5 minutes. Flip the patties and immediately top each with a slice of cheese, followed by bacon and caramelized onions.
Double stack the patties and place them on brioche buns, spreading burger sauce on the buns as desired. If you like, toast the buns on the griddle before assembling.
Wrap the assembled burgers tightly in foil and let them steam for five minutes before serving.