ML and FL love each other a lot and really want to be together but fate/things/people are actively trying to stop them from being together. Can be a tragedy (but dont give me spoiler. Dont tell me if its a tragedy or not). No matter what they do, things are not in their favor.  

Example:

Hotel Del Luna

Gyeongseong Creature

Angel's Last Mission Love

Till the End of the Moon

Love and Redemption

Moon Lovers

Goblin

Crash Landing On You

You Who Came From the Stars

All your favourites are from Korea, thus I thought you'd probably especially look for Korean dramas?
some recs; 
Pinocchio 
My Name - this has sort of 2 star crossed "couples". one that actually ends up together and another one with one hell of a chemistry but welp. Not used. Still its a great one
The Smile has left your eyes
Just Between lovers
Uncontrollably Fond
Descendants of the Sun
The Winter the Wind blows
Train
Cruel City
Money Flower - this is a little more tricky. It is the best revenge drama in korean land you will ever find. It is extremely complex, super well developed, and very unusual. However it is very political so romance is not the main story. But it fits the bill.

**Love Between Fairy and Devil

Queen for Seven Days

Hotel King

My Journey to You

The Ingenious One

Come and Hug Me

Scent of a Woman

  • Come and hug me
  • Queen for seven days
  • I'm sorry I love you

i didnt see anyone mention that one but 

Extraordinary You 

it is the best "star crossed lovers" k drama ive seen for now and it is done in a pretty unconventional way, i recommend it!