KDramas Only: Dominant, Possesive Male Lead

• Devil
• Last Empress (emperor)
• What's Wrong with Secretary Kim 
• Scarlet Heart Ryeo
• Mask 
• That Winter the Wind Blows 

• A Korean Odyssey | Though I would recommend that you don't binge watch it. You'll also have to go in with an open mind since the CG is very cringy.
• Black | I highly recommend this one if you don't mind a story with a side or romance. If you're looking for romance with a side of story, then this might not be your cup of tea.
• Cheese in the Trap 
• City Hunter 
• Falling for Innocence 
• Hello Monster | I wouldn't tag the ML as controlling, but he does usually have the upper hand when it comes to his interactions with the FL.  
• Just Between Lovers | ML is a good-hearted person, but rough around the edges. Not sure if this one is what you're looking for, since he's a bit possessive but not controlling.
• Kill Me, Heal Me | 2ML (one of the ML's personalities) fits the bill.
• Lawless Attorney | Wouldn't tag him as controlling, but he is dominant and possessive, while still being respectful of the FL. He treats her as an equal partner first and foremost but loses his cool when she's in danger.
• +1 to Moon Lovers: Scarlet Heart Ryeo | But this one is a reverse-harem, so you'll need to be in the mood for a FL that bounces around.
• My ID is Gangnam Beauty | He's possessive, not controlling.
• Noble, My Love | Fits the bill perfectly.
• Oh My Venus | Sort of fits the bill.
• She Was Pretty | Fits the bill perfectly.
• Secret Garden | Fits the bill perfectly.
• Something About 1 Percent | Fits the bill perfectly.
• The Beauty Inside | Fits the bill perfectly.
• The Greatest Love | Fits the bill perfectly.
• The Master's Sun | Fits the bill perfectly.
• The Smile Has Left Your Eyes | Fits the bill perfectly.

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.