In Time With You
About two best friends since high school make a bet to see who marries first. The female lead is insecure about her single status at the age of 30 while the male lead is very quiet, respectful and intelligent. You later find out that both of them have had many partners over the course of their lives since high school, but none of them have really been good. The show focuses on the female lead's journey to realizing that her one true love has been right beside her the entire time.
The Pursuit of Happiness
Made by the same people who did In Time With You. This time two strangers meet and become landlord and tenant. They each start off explicitly saying they have a one sided love to another person. However as time passes by, they become good friends who get too comfortable with each other. What I mean by this is they know what each other likes, they buy/make dinner for each other, help one another when they're drunk or sad. The female lead in this one, again, goes through the motions of realizing that the person she loves is not the person she longs for but the person that was right beside her from the very beginning.
I know you asked for J or K dramas but give these a shot, they are very good
