Start by thinly slicing the onion and beef. If possible, partially freeze the beef for about 30 minutes before slicing; this will make it easier to achieve those ultra-thin slices.
In a large skillet over medium heat, add the vegetable or olive oil. Allow it to heat up until shimmering.
Add the thinly sliced onion to the skillet and sauté for about 5-7 minutes, or until they become soft and translucent. Stir occasionally for even cooking.
Once the onions are ready, add the thinly sliced beef to the skillet. Stir-fry the beef for about 3-4 minutes until it's browned and just cooked through.
Sprinkle the sugar over the beef and onions. Pour in the mirin, soy sauce, and dashi or beef stock. Stir well to combine all the flavors. Let it simmer for about 5 minutes, allowing the sauce to reduce slightly.
While the beef mixture is simmering, you can prepare the eggs. In another pan, gently fry the eggs sunny-side up or to your preferred doneness.
To serve, place a generous scoop of cooked short-grain rice in each bowl. Top the rice with the beef and onion mixture, followed by a fried egg.
Finish with a sprinkle of chopped scallions and toasted sesame seeds, if desired. Serve with beni-shoga on the side for that extra zing!
