Cook the bacon in a wide skillet over medium heat for 8 to 10 minutes until crisp, then drain it and leave 1 tablespoon fat in the pan.
Add the red onion and cook for 8 minutes, then stir in the brown sugar and vinegar and cook for 3 minutes until glossy.
Divide the beef into 4 thick patties, dimple the centers and season them with the salt and pepper.
Heat a cast-iron skillet over medium-high heat and sear the patties for 4 minutes on the first side.
Flip the patties, reduce the heat to medium and cook for 5 to 7 minutes until the centers reach 160°F.
Top each patty with cheddar for the final minute and cover the skillet until the cheese slumps over the sides.
Toast the buns in the bacon skillet for 1 minute, then spread them with mayonnaise.
Build each burger with arugula, one patty, 2 bacon slices and a spoonful of the sweet-sour onions.