Japanese rolled omelet is called tamagoyaki or dashimaki. It's also known as a Japanese-style egg roll.
There are many types of tamagoyaki. Some are sweet and some are salty. Also, it can be added fillings in to make it colorful. Tamagoyaki is usually cooked in a rectangular omelet pan.
see how to make tamagoyaki : http://www.youtube.com/watch?v=ja8fCHS4aRI
It used to be said "To judge which sushi shop is good, you can judge by their tamagoyaki" ... However, nowadays we cannot since there's company (manufacturer) deliver tamagoyaki to some of sushi shop.
At this shop, I was able to tell that they made this by their own since it's so fresh, so juicy ... so good ... melt in my mouth !!!