Heat 2 tablespoons of the oil on one side of the griddle over low heat.
Add the onion and cook, covered, stirring occasionally, until soft and browned, about 15 minutes. Leave the heat on low.
Heat the remaining 2 tablespoons of oil on the other side of the griddle over medium-high heat. Add the ribeye in a single layer, and cook, stirring occasionally until no pink remains, about 3 minutes. Reduce heat to low.
Stir the onion into the beef and season generously with salt, pepper, and the garlic powder.
Divide the meat mixture into 4 portions on the griddle, and top each portion with 1 slice of cheese. Cover and let it melt, 1 to 2 minutes.
While the cheese is melting, slice open the rolls and place cut side down on the other side of the griddle. Toast until lightly browned, about 30 seconds.
Scoop the meat and cheese mixture into the buns and serve.
Notes
Finding sliced ribeye--If you have access to a Korean market, it's an excellent place to find pre-sliced ribeye at a reasonable price.
Slice it frozen--For the easiest slicing, cut your beef into strips when it is still slightly frozen.