Interesting question, but.. why are you asking for k drama only? I'm getting curious now which k drama-actor set the example.
If you're asking for dominant, possessive male leads in k drama, these guys are difficult to find. The typical Korean male lead turns out to be arrogant, bossy, aloof. Perhaps you should try some Chinese series to see more passionate male leads like: Cruel Romance (2015), Lady & Liar (2015) or Siege in Fog (2018). The only k drama I can think of is a Chinese remake: Moon Lovers Scarlet Heart Ryeo (2016).
However Korean dark male leads can be seen plenty in revenge drama. The main difference being "dangerous with a dark past" or "dominant and controlling".
Dangerous with a dark past
Time Between Dog and Wolf (2007)
A Man's Story (2009)
Bad Guy (2010)
Cruel City (2013) ( highly recommended!)
Dominant and controlling
A Love to Kill (2005)
A Man Called God (2010)
Liar Game (2014)
I hope you'll find what you're looking for. Please let us know.