Yes, it is pretty popular in Japan. Because the egg yolk looks like the full moon, several restaurants in Japan, including McDonald's, sell Tsukimi (moon-viewing) burgers like this one during Harvest Moon season.
Is there egg on that burger. I'm not a fan of eggs so I'm probably never going to eat it like that but has anyone actually tried egg on burger?
Red Robin does it with most of their burgers on the menu, and my god the runny yolk goes VERY well with the meat, seasonings, and the toppings. For those that love eggs and burgers I HIGHLY recommend getting fried eggs on your burgers!