Slice the onion into thin rings. For pickled onions, heat ½ cup of water in a large glass measuring cup. Stir in sugar, salt and vinegar until the sugar and salt dissolve. Place the onion into a jar or small bowl, and pour the vinegar mixture over the onions. Set aside. Extra onions can be stored in the fridge for up to 3 weeks.
Open the can of chiles, and slice the cheese into 8 small slices, or 4 larger ones. Butter the cut side of the buns.
Start to heat up a pan, if cooking on the stovetop, or a grill. Divide the ground beef into four equal portions, and form patties approximately the size of the hamburger buns.
After the pan or grill heats up, place the patties in the pan, season as desired, and cook for 3-4 minutes.
Flip the burgers over, and cook for 2 more minutes. Top each burger with a scoop of the chiles, then top the chiles with the sliced cheese. Cover the pan (or close the grill) and cook for 2 more minutes.
Remove the burgers from the pan and wipe the pan clean. Toast the buns, butter side down, for 1-2 minutes. Or toast them quickly on the upper rack of the grill while the cheese is melting.
To serve, top with lettuce, tomato, onion, mustard, ketchup, mayo or whatever you prefer.