Great Modern Korean
There must be LA equivalents.
No, not really at the level of Danji or Hanjan.
Closest you'll find is a place like A-Frame or Chego, the latter being quite casual (in comparison to Danji/Hanjan) and if you go now you'll enjoy a slow moving 1/2 hour line.
When The Line Hotel goes fully operational in Koreatown, Roy Choi has two restaurants opening up there, so those might be possibilities, but who knows ...
I would give up sex for a day if a place like JungSik opened up in LA.