This rolled omelet takes a bit of practice to master. Use the tool you’re most comfortable handling; forks, small offset spatulas, and chopsticks work well. Removing the skillet from the heat gives you some wiggle room to slowly roll and shape the omelet and oil the skillet.
How to Make It
Whisk together eggs and egg yolk in a bowl until thoroughly blended. Add master dashi and soy sauce; whisk to combine. (There will be about 2 cups egg mixture.) Set aside.
Place 1 1/2 tablespoons sesame oil in a small bowl. Fold half of a paper towel into a square, and submerge in sesame oil.
Heat a rectangular tamago pan or an 8-inch nonstick skillet over medium-high. Rub the oiled paper towel inside and up the sides of skillet. (Pour any excess oil in skillet back into bowl, and do not discard paper towel.)
Add a drop of the egg mixture to skillet; once the drop sizzles, pour in 1/4 cup of the egg mixture, and swirl the skillet to evenly coat. Cook until egg is almost set, 45 to 60 seconds, popping any air bubbles that arise using chopsticks. Remove skillet from heat. Using chopsticks or a small spatula, loosen edges of egg crêpe from skillet, and gently and tightly roll up omelet toward pan handle; push rolled omelet to opposite end of skillet. Rub skillet with oiled paper towel around omelet, and return to medium-high heat. Add an additional 1/4 cup of the egg mixture to skillet; slightly tilt the skillet away from you while lifting the omelet so that the uncooked egg mixture seeps under and covers the entire surface of the skillet, and then lower the omelet into skillet. Cook until the new egg crêpe is almost set, 45 to 60 seconds, using chopsticks to pop any air bubbles that form. Remove skillet from heat. Using chopsticks or a small spatula, loosen edges of new omelet crêpe from skillet; gently roll the omelet toward pan handle, gathering egg crêpe and forming a larger omelet. Push rolled omelet to opposite end of pan and repeat with oil, egg mixture, and rolling motion two more times. Continue cooking omelet until browned, about 1 minute per side. Turn out omelet onto a work surface, and let rest 5 minutes.
If needed to help hold its shape, turn out the omelet onto a lightly moistened wooden sushi mat; wrap the mat around the omelet, gently pressing to shape it into a cylinder.
While omelet rests, repeat Steps 2 through 4 using remaining 1 1/2 tablespoons sesame oil and 1 cup uncooked egg mixture.
Slice each finished omelet crosswise into 4 even pieces. Serve warm or at room temperature.