In a small bowl, combine the dashi, salt, soy sauce, sugar, and water. Mix until everything is dissolved.
In a medium bowl, beat the eggs and add the seasoning mixture. Mix until well-combined.
Heat a tamagoyaki pan over medium-high heat. Brush a thin layer of oil on the pan.
Pour a third of the egg mixture into pan and quickly swirl to cover the entire pan. When the egg is half-set, gently roll the egg.
With the rolled egg still in the pan, pour in another third of the egg mixture. Lift up the rolled egg and let the mixture to flow under it. When the egg is half-set, roll the omelette toward you. Repeat with the rest of the egg mixture.