Heat a small (8 inch) non-stick pan on medium-low heat.
Beat eggs, sugar, mirin, salt, sesame oil and soy sauce together with a fork. Don't use a whisk - the mixture should not be foamy.
Using a crumpled paper towel, brush the heated pan with a little oil. Put in 2 to 3 tablespoons of egg mixture in the pan. Lower the heat slightly and cook until not quite set, but not runny.
Using a non-stick spatula, roll it up and push to one side of the pan.
Brush the exposed part of the pan with more oil. Put a couple more tablespoons of egg in the pan. Spread it around, lifting the rolled, cooked egg so that the uncooked mixture flows below it.
Cook until almost set, then, starting with the cooked, rolled egg, roll back to the opposite side of the pan. Repeat until the egg mixture is used up.
Remove the omelet from the pan and place it on one end of a clean, slightly moistened dishcloth with the seam side of the omelet down. Roll it up tightly, but gently. Set aside to cool completely.
Unroll and slice at an angle with a sharp knife.