Warm a generous splash of neutral oil in a large skillet set over medium-high heat. Once the oil shimmers, add the thinly sliced onions. Cook them slowly for about 10 minutes, stirring frequently, until they soften and begin to turn translucent with a light golden edge.

Stir in the sliced beef and sprinkle over the sugar. Sauté the mixture just until the beef loses its raw color and takes on a light sear. Pour in the mirin, soy sauce, and your chosen stock. Bring the liquid to a gentle boil, then reduce to a simmer. Let it cook for 10 to 15 minutes, allowing the flavors to meld and the liquid to reduce into a flavorful, light sauce. Taste and adjust the seasoning with an extra dash of soy sauce if needed.

Meanwhile, in a separate skillet—preferably cast iron or non-stick—add a bit more oil and fry the eggs sunny-side up. Cook them in batches if necessary, making sure the whites are set while keeping the yolks beautifully runny.

Once the beef mixture is ready, spoon the warm rice into four bowls. Evenly divide the simmered beef and onions over the rice. Gently top each serving with a freshly cooked egg. Finish by sprinkling chopped scallions and, if desired, toasted sesame seeds for extra aroma and crunch. Serve immediately while hot.