Make the egg mixture: Add the eggs, sugar, water, and soy sauce to a mixing bowl. Whisk until the mixture is smooth and evenly combined.
Prepare the pan: Lightly oil a tamagoyaki (rectangular) pan using a folded kitchen paper. Make sure the oil is spread evenly. To check if the pan is hot enough, drop a little egg mixture with chopsticks—if it cooks right away, the pan is ready.
Cook the first layer: Pour one-third of the egg mixture into the pan, tilting it to spread evenly. When the egg is about 80–90% cooked, roll it up from the near edge toward the far side in three folds. Don’t worry if the shape isn’t perfect—this layer will be on the inside.
Cook the second layer: Add another one-third of the egg mixture. Lift the rolled egg slightly with chopsticks so the new mixture flows underneath. Once mostly set, roll the omelet back toward you. You can also use a spatula if that’s easier.
Cook the final layer: Push the rolled omelet to the far side of the pan. Add the remaining one-third of the egg mixture, oiling the pan again if needed. When mostly cooked, roll the omelet toward you one last time. Shape it gently with chopsticks or a spatula.
Finish and serve: Remove from the pan, let it cool slightly, then slice into bite-sized pieces. Serve warm, pack into a bento box, or enjoy with grated daikon radish on the side.