Wrap a small bundle of enoki mushrooms with a slice of ribeye beef, rolling tightly. Repeat until all mushrooms and beef are used. Set aside.
In a small bowl, combine chicken stock, soy sauce, sesame oil, mirin, sugar, and black pepper. Set aside.
Heat oil in a pan over medium-high heat. Add the sliced onion and sauté until soft and translucent, about 3 minutes.
Arrange the beef-enoki rolls on top of the onions. Pour the sauce over them. Cover and simmer for 3 minutes.
Remove the lid, pour the beaten eggs over the rolls. Let cook uncovered for 1 minute, or until the eggs are just set.
Serve hot with steamed rice. Garnish with spring onions and sesame seeds.
