Highly engaging character

Hello!

I'm not sure that's really what you're looking for, but here are some Japanese recommendations with peculiar guys (not sure that they are all that engaging though, i guess this kind of interest is a question of point of view):
- "Dokushin Kizoku", male lead is a kind of Japanese gentleman (the perfect man from my very own point of view)
- "Legal High", the male lead, very peculiar.
- "Kagi no kakatta Heya" : the main lead is very special, but probably not in the way you wanted.
- lately, "Kizoku Tantei" has a peculiar male lead, but the drama is not that good (yet it kept me interesting till the end), and just before there was "IQ246" who had the same kind of character.
- I was personnaly fascinated by Koizumi in "Juken no Cinderella", but he is not a very likable character
- maybe main lead in "Hero" (japanese serie)
- "Kazoku Game" : main lead
- "Nazotoki wa, Dinner no ato" de : male lead.

Hope it could help.

Stranger (2017)/Secret Forest, I wouldn't say "interesting" though, but he's very....different in a way lol

For funny/hilarious (depends on your tastes):

Jdrama - Kekkon Dekinai Otoko, Unubore Deka, Sexy Voice and Robo (both leads), Fake Couple (female lead especially)

Kdrama - Chief Kim, W  Two Worlds.

Cdrama - Love me if you dare - wallace huo's character!, Maybe Love o2o, main lead is your typical smart AND athletic good looking guy, but he doesn't "bully" the main lead girl like all the others out there lol. 

edit* almost forgot cdrama