Trim the bottom 1-2 inches off the enoki mushrooms, rinse, and separate into small bundles.
Lay out a slice of beef and roll each enoki bundle tightly inside. Repeat until all are wrapped.
Mix all sauce ingredients in a bowl and set aside.
Heat oil in a large skillet over med-high heat, add onions, and cook for 3min until softened.
Place the beef rolls over the onions in a single layer, pour in the sauce, cover, and bring to a boil. Reduce heat to low-med and simmer for 3min (until beef is cooked through).
Uncover, pour whisked eggs over the rolls, cover again, and cook for 1min.
Salt to taste. Remove from heat, garnish with green onions and sesame seeds.