I love romcoms with a dash of fantasy/supernatural and a little bit of melodrama. Examples are Secret Garden, My Love From Another Star, My Girlfriend is a Gumiho, Rooftop Prince and Master's Sun.  But I also like romantic comedy dramas without fantasy/supernatural genre like Emergency Couple, Cunning Single Lady, Witch Romance (currently watching). I haven't watch ANY Japanese dramas because they talk too fast. But feel free to suggest K/J/T dramas. I would love to try any new things since its my dayoff tomorrow. Lol. XD
Who Are You? (MBC) This is the 2008 version with Go Ah-ra and Yoon Kye-sang, not to be mixed up with the 2013 TvN version.
Queen In-hyun's Man I'm not sure if this is an actual rom-com, but I think it's close.
Soulmate I wouldn't call this supernatural drama because the rules of the world never define what is happening.
High School Love On
Supernatural romantic comendies i can recommend you are blade man, the girl who sees scents and oh my ghost. there are dramas that i finished recently and i really enjoy them.
Now without supernatural theme are just you (t-drama but you can give it a try) and protect the boss 
Korean:
Romcom/fantasy/supernatural
- Bride of the century (this one has a little bit of supernatural element, really good highly recommend)
- Queen in hyun's man (similar to rooftop prince, time travel fantasy)
- Blood (fantasy vampire, medical melodrama, don't know if it classifies as romcom)

Normal romcom
- Cheer up/sassy go go (this one recently finished, highschool romcom, really short 12 eps, really good high recommend)
- Panda and Hedgehog (really cute romcom about cake/sweets making)
- City Hunter (similar to healer though i liked this one better, great action with romance)

I don't know if you watched historical ones but I highly recommend:
- 'Gu family book' --> fantasy romance, though i would say it's more of a melodrama however beautiful love story. If you have time please try. 

Taiwanese:
They don't make a lot of fantasy/supernatural ones:
- The legend of the Brown sugar Chivalries (probs the only one i've seen close to supernatural, romcom)

Normal romcom:
- My lucky star (one of my early dramas, i love the symbolism of jewelry in this drama)
- Prince turns to frog (one of the old classics, love the story though its full of cliques however for a drama this old the cliques weren't cliques back then)
- Smiling pasta ( a true romcom, barely/no melo parts, just really sweet and cheesy)
- Autumn's concerto (classic, not much of a romcom more melo drama oriented but really good)
- Pleasantly surprised (nice romcom about french cuisine)
- Love keeps going (short 13ep romcom with a bit of angst in the middle)
- Just you (sweet romcom between boss and employee )
- Fondant garden (romcom about sweets)

Japanese:
I personally haven't seen a lot of Jap dramas yet, I'm just getting into it.
The only really good romcom I know is:
- Itazura na kiss; Love in Tokyo 1+2 (this one is the jap remake, my favourite version of the story, really good, 2 seasons)

While I'm at it, recently I watched a really good thai romcom. I'll just put it down for you to consider.
- Ugly duckling series: Perfect Match (this drama is only 9eps, short romcom, really cute with a nice meaning behind it)

Sorry for the long list, hope you enjoy.
fantasy/supernatural and a little bit of melodrama? I think I Hear You Voice fits perfectly (and it has an awesome OST too)
 
*For a quick, simple rom-com, Noble, My Love is a web series that is completely binge-worthy

*For something a little new Scarlet Heart is a well-known historical C-drama. It has 40 episodes, but don't let that scare you. I always feel that J-and C-dramas are always more fast-paced and shorter than K-dramas. At the end of the series I was wishing there were more eps. (but don't let that feeling fool you into watching the sequel. Now THAT was terrible!)
Seems like many of those who comment on this thread, watch more korean than Japanese, so Ill give you some Jdorama recommendations! :D
I enjoyed watching all of these.

Without fantasy.

Buzzer beat
Kimi wa petto 
Last cinderella
One pound gospel
Pin to kona
Rich man, poor woman



With fantasy.

Yamato nadeshiko shichi henge
Q10