Blueicus identified both dishes and gave them their right names. I want to add the proviso that spelling can be variable.
When it comes to the ultimate texture of gyren jim, it is whatever the cook makes of it. Steamed slowly and with the right ingredients it is as silky as the silkiest chawanmushi.
Texture depends on four things: Dilution of the egg; what's in the dilute; the amount of egg in the cup, size of the cup, and type of cup; and the heat of the cook. A good, average dilution level is 1 cup of water to every 3 eggs. Slightly less water will make the custard firmer, slightly more will make it softer (silky). The water can be used plain, flavored, or with something that will effect the texture by holding a more dilute mixture together. For instance, kombi may be cooked in the water, with the kombi discarded and the water reserved. A smaller cup holding the equivalent of 1 egg (plus dilute, and with a little room for the slight "rise" during cooking) is easier to manage than a larger bowl. Sometimes large, preheated stone bowls are used, and these will result in a very firm texture. The custard should be cooked with the heat of the steam alone. That means the water should be at an easy simmer -- not a full boil. A full boil is a sign that you're introducing more heat than necessary into the system.
Blueicus referred to the Japanese practice of floating a bit of liquid on top of the custard. This protects the surface from drying as the egg is brought from kitchen to table and while it sits on the table. As far as I know this is one custom that never made it into Japanese cuisine.
There is quite a bit of commonality in Japanese and Korean foods. Over the past eight centuries, Korea spent several hundred years in conflict with Japan, in close association, but mostly as a colony. Japanese colonists brought their food to Korea and Koreans were shipped to Japan to work as domestic servants. An unfortunate consequence of this history is Japanese bigotry towards Koreans. Into the eighties this was widespread and brutal. It's changed a lot over the last couple of generations, is not nearly as common as it was, but still exists in Japan as a social and economic force. It is directed not only at new immigrants but at families who have lived in Japan for hundreds of years. Of course, ethnic bigotry is not a uniquely Japanese phenomenon, we have more than our share here too.
However, a happy consequence is the interaction of cuisines. Zerizushi
with a slice of sashimi
laid across a small, slightly compressed, glob of rice is undoubtedly a purely Japanese phenomenon first introduced in Edo. The history of eating sashimi in Asia is lost in history. Since forever and started by who knows. To the best of my knowledge maki
(cut roll) came after zerizushi
, but their origin cannot be localized. Given the relationship of Korea to Japan at the time sushi became popular, these might actually be Korean. One aspect of the interaction is the Korean "Japanese Restaurant." These places are usually organized around sushi
and a wide variety of Korean interpretations of Japanese dishes, and a similarly wide variety of purely Korean food. It's a very old tradition in Korea, going back to the earliest days of colonization. On a personal note: This is one of my favorite types of cuisine. So much so, that if I were forced to choose one forever -- it might well be the one.
PS Here's a link to a good site for Korean food, including recipes for both of your new discoveries: http://mykoreankitchen.com/2007/04/1...s-gyeran-jjim/