Mix all the ingredients together (except the oil) very, very well.
Keep the tips of your cooking chopsticks on the bottom of the bowl when you mix, and try not to introduce air bubbles. Mix well to whisk the egg whites properly.
Spread oil in a frying pan and heat. Wipe excess oil with paper towels. I added some tips for adjusting the heat level in Hints.
Press the bottom of the pan on a tightly wrung out moistened wadded up kitchen towel to even out the heat.
Spread a bit less than 1 ladleful of the beaten egg in the frying pan, and spread it around the whole pan. If any air bubbles form, pop with chopsticks.
When the surface is soft set, fold it into thirds using chopsticks.
Push the folded egg to the far side of the pan. Spread some oil in the open space of the pan using the oil-soaked paper from Step 2. Press the bottom of the frying pan on the moistened kitchen towel again as in Step 3.
Pour in some beaten egg as in Step 4. Hold the rolled egg up a bit and tilt the pan to let the uncooked egg flow under it.
Repeat Steps 5 to 7 until all the beaten egg is used up.
Wrap the cooked tamagoyaki in a sushi rolling mat and leave it as-is for a while. The tamagoyaki is done. If you match up the edges of the mat to the corners of the tamgoyaki when you wrap it, the surface will have a clean spiral.
Story Behind this Recipe
In our family, we have a home parties with hand-rolled sushi every month on payday. My husband is very picky about tamagoyaki and says "store-bought is better!" To shut him down, I adapted various recipes to my own preferences and taste. When he said "Yummy! This is the real thing!" I was so happy.
There is a fair amount of sugar in this so it burns easily, but cook the omelette over as high a heat as you dare!! To control the heat, lift your pan up to put distance between the pan and the flame, rather than adjusting the flame itself. If you have an induction cooker, set it at 160°C (the setting for deep frying) and it should work well.