Well I have been into this kind of plots since my puberty lol. But I didn't know how to find that type of drama, sometimes I encountered my perfect plot but couldn't find other ones like it; let me mention some of the ones I remember:

  • Healer

Healer was the first kdrama (with the badass dude kind of plot IDK) I found that fitted perfectly into my list, then I noticed that I liked: the kind of relationship were you dont expect the ML to ever fall in love.

The I encountered other dramas like Healer...

  • The K2
  • ManToMan

And that's it ;;

I know I'm looking for series where:

  • The dude is a badass daddy 
  • Unbelievable that he can fall in love
  • He's good at what he does

Recently I saw A Korean Odyssey, even though this is not a "professional killer" falls in love it's similar.

Since I can't name an exact tag or genre I see this task quite difficult so I'm resorting to your guidance -^-, thank so much.

Check out:

  • Mr. Sunshine
  • Heartless city
  • Bridasl Mask
  • City Hunter
  • The Disguiser
  • Iris
  • Time between Dog and wolf
  • Sweety Spy
  • The Crown Princess
  1. Once Upon a Time... In My Heart 
  2. Life's Waves 
  3. The Cupids Series: Kammathep Hunsa 
  4. Black & White 
  5. Our Times 
  6. Bad Guy 
  7. Bring It On, Ghost 
  8. Confidential Assignment  This doesn't have romance but I thought you may like it
  9. Gangster Lover
  10.  Going by the Book   This too doesn't have romance but the male lead will surprise you by doing unexpected things.
  11. Powerful Opponents The roles is inverted
  12. Righteous Ties
  13. The Man From Nowhere  No romance too
  14. Cruel Romance
 Czakhareina:

Check out:

  • Mr. Sunshine
  • Heartless city
  • Bridasl Mask
  • City Hunter
  • The Disguiser
  • Iris
  • Time between Dog and wolf
  • Sweety Spy
  • The Crown Princess

I already saw Mr.Sunshine, Cruel city and City Hunter; forgot to add these hehe. I fell in love with cruel city though sadly I'd doesn't have that much romance... but thank you so much!

 ahsaaful:
  1. Once Upon a Time... In My Heart 
  2. Life's Waves 
  3. The Cupids Series: Kammathep Hunsa 
  4. Black & White 
  5. Our Times 
  6. Bad Guy 
  7. Bring It On, Ghost 
  8. Confidential Assignment  This doesn't have romance but I thought you may like it
  9. Gangster Lover
  10.  Going by the Book   This too doesn't have romance but the male lead will surprise you by doing unexpected things.
  11. Powerful Opponents The roles is inverted
  12. Righteous Ties
  13. The Man From Nowhere  No romance too
  14. Cruel Romance 

Thank you I'm not that much into chinese dramas but I'll give it a try to some of them ^^

In addition:

With ROMANCE, but which left some unsatisfied:

  • Moon Lovers: Scarlet Heart Ryeo | ML can fight and has been through so much, it's a miracle he allowed someone into his heart. However, a lot of people were dissatisfied with this one (especially regarding the romance). So if a good romance is a must, check some reviews beforehand to see if it's what you're looking for.
  • A Beautiful Mind | ML is a psychopath, but he still manages to fall in love. First half it's a little slow, but picks up during the second half. Can't say the FL is great, but she's decent.
  • Cheese in the Trap | ML gives "psycho" vibes, which makes the series interesting. However, if you want to watch it for the romance, it might not satisfy you.

SUBTLE ROMANCE:

  • The Ghost Detective | I loved him.
  • Terius Behind Me | Similar vibes to Man to Man, but MUCH better.
  • The Last Empress | Similar to City Hunter. I'm considering Na Wang Sik as the ML, but others consider the Emperor as the ML. The Emperor, of course, is not strong.

NO ROMANCE:

  • Kingdom | A crown prince fighting zombies. Enough said.
  • The Guest | Both MLs are awesome, but there's no romance.
  •  Voice & Voice 2 | Similar to a mix between Cruel City and City Hunter. No romance. But both MLs are badasses. The FL (same in both seasons) is actually the best character, though.

OH GOD that's a long list, thank you so much and sorry for taking a while to answer. Well I didn't add them in the list but I've already watched some of the dramas you recommended 3GGG here some of them hehe:

  • Black
  • Lawless attorney
  • Where Stars Land
  • You Who Came From The Stars
  • Moon Lovers

And that's about it, I also dropped some of them (which I'm planning to rewatch of course for example Terius Behind Me )

But great, you have such good taste, I love you. I added 3 of your recommendations to my watch later ^^: Hello Monster, Cheese In The Trap and Ghost Detective.

 Alyx:

OH GOD that's a long list, thank you so much and sorry for taking a while to answer. Well I didn't add them in the list but I've already watched some of the dramas you recommended 3GGG here some of them hehe:

  • Black
  • Lawless attorney
  • Where Stars Land
  • You Who Came From The Stars
  • Moon Lovers

And that's about it, I also dropped some of them (which I'm planning to rewatch of course for example Terius Behind Me )

But great, you have such good taste, I love you. I added 3 of your recommendations to my watch later ^^: Hello Monster, Cheese In The Trap and Ghost Detective.

Not a problem! Terius Behind me is a cute drama, but I watched it while it aired, so that could certainly impact my enjoyment. I've found not all dramas can be binged. 

Hello Monster is in a similar vein to Lawless Attorney, in that you'll get a balanced dose of crime+ action + romance. Except that the bad guys in the former are perhaps more interesting. 

The Ghost Detective is more in the vein of a light version of "Black", in that the leads are working against ghosts and a supernatural enemy. The antagonist is interesting though. But keep in mind that dramaland demands that our protagonists should make some questionable choices to make the plot last XD.

Cheese in The Trap is unlike any other I've seen. It leans more towards the psychological than romance, so it stands out as something very different from what you might expect. Of course, some people liked it and others hated it. But I think it's going to be something you'll remember either way :).