You can get pre-thin-sliced beef at an Asian grocer; if you cannot find pre-sliced beef, par freezing the rib-eye steak will make it easier to slice thinly with a sharp knife.
Combine all the marinade ingredients and toss in the thin-sliced beef. Let marinade for at least an hour. Because the beef is thin-sliced, you don't need to marinade it for that long - a couple hours is plenty.
In a hot pan, or cast iron skillet, heat a little oil and fry the meat in batches. If you cook too much beef at once, your pan will accumulate with too much liquid which will prevent the beef from searing and browning (think boiled/steamed instead). So if you have a lot of liquid accumulating, dab it away with some paper towl or drain some of it off. Fry until all the beef is cooked.
Serve hot with a side of rice; garnish with chopped green onion and a sprinkle of sesame. Enjoy!