I often come across this kind of carrot cake in North America. It is so moist and delicious. Since it doesn't use a lot of sugar or oil, it's also kind-of healthy.
I ate this often while living in Canada. I wanted to try to make it myself, so I found a recipe on an American recipe site, used ingredients that I had on hand, and decreased the sugar and oil.
The nuts and dried fruits are optional.I added maple syrup for extra flavor, but it's also optional. I added rum to the icing, but vanilla also works well.
Enjoy Japanese food around the world.