recommendation: a drama where the male lead is obsessed with the female? ;)

Boss and Me (aka. Shan Shan Comes to Eat) fits your description perfectly. Plus it's light and fluffy.

Hey, thanks for reviving this recommendation thread, over a year later! 

First, for others that are looking for that kind of hero (since it seems quite popular): I second Boss & Me where the male lead absolutely fits the description, as well as Discovery of Romance and Oh My Ghostess, although they focus a bit less on that aspect (still pretty obsessive heroes though, hehe). 

@Roisina: thanks for your other three recs -- I'm currently watching Second time twenty years old again, and I get what you mean! (though he sure is childish about it, hahaha)

My heart twinkle twinkle! The storyline might not sound convincing at the first moment, but as the story develops it has one of the most interesting male leads
that I've seen so far. He's the embodiment of obsession and what I really like about this drama is that his character stays ambivalent. Till the end you don't know if you should hate him or love him.

I'm aware that I'm answering to my own question (:^p) but in case anyone is still looking for shows with this theme, I just finished a web drama that's actual plot is all about the hero falling in love obsessively: High-end crush. It's very simple and like many others I'm no Jin Se Yeon fan, but I enjoyed it nonetheless ;^)

There is another web drama which fits the bill, It's about a chaebol falling in love with a vet and pursuing her obsessively. It's called Noble my love. It's hilarious with a strong female lead too! 

Not a drama, but a Korean movie called Obsessed (2014). A warning: it's not a light watch, quite steamy and dark, definitely for mature audiences.

Some spoilers ahead:

We don't know if he is a possessive type, but is very obsessive, however you only find out the level of this guy's obsessiveness in the last 30 minutes of the film.

"Manhole"! It's currently airing and the male lead is ridiculously in love with the female lead. However, in the present time, she is getting married which eventually makes him go back in time - by falling into a manhole - to change the past (+future). Some people don't like how much he's overreacting but I love it. It's lots of fun! :)

Second Beating Again and Noble, My Love. 
I would also add Strong Woman Do Bong Soon to the list. 
There is a guy with stalking tendencies in My Mr. Mermaid, but he is not the main male character.