Preheat a seasoned grill pan or griddle over medium heat.
Assemble this sandwich just as you would a traditional grilled cheese sandwich: spread 1 slice of bread with some red onion mayo, then top with 2 slices cheddar, the bacon, the apple slices, then 2 more slices of cheddar, finishing with another mayo-slathered slice of bread.
Butter the outsides of the bread and transfer to the hot grill.
Grill about 3 minutes per side, since this sandwich is so thick.
Remove to a cutting board and cut the sandwich in half on the diagonal to serve.