Preheat a grill or grill pan to medium-high heat. If you're not using an outdoor grill, preheat a second grill pan over medium heat (for a side griddle).
Gently mix together the brisket, short rib and sirloin in a large bowl. Divide the mixture into 4 equal pieces and gently form into burgers, being careful not to pack too tightly.
Season both sides of the burgers with a good amount of salt and freshly ground black pepper.
When the grill or first grill pan is at medium-high, place the burgers on the grill and cook to your desired temperature, 3 to 4 minutes per side for medium rare. Add a piece of cheese to each burger and cook for another minute or so until it is melted.
In the meantime, spread the mayo on the cut side of the buns and place them over medium heat or on the secondary grill pan to toast.
Build the burgers by placing a burger on each bottom bun and top with 2 pieces of bacon, some red onion, pickles and mustard.