You can try:-
Bloody Romance - Fantasy wuxia drama about a group of female assassins and their male servants. Take note drama made the FL with a kind heart who refused to kill unless it is necessary, most of the time she used intelligence to complete her assignments (some viewers didn't like this). They both fell in love with each other, but FL confessed to him first. ML had to kneel overnight too, but considering what happened, he should probably have kneeled for a week.... there's much angst in this drama.
Rattan - Contemporary fantasy about a plant alien FL who came back alive after many years, and the human ML who reluctantly served her, and in process fell in love with her....
The Other Half of Me and You - Contemporary fantasy drama about a gender swapped parallel world. ML did the wooing.
Rational Life, Find Yourself - Noona workplace romances, MLs chased FLs too.
Hotel del Luna - Contemporary fantasy about a afterlife hotel, FL is the hotel guardian and ML a normal human who was chosen to worked as Hotel Manager there. Can't remember who chased who first...
I watch mostly Chinese dramas, unfamiliar with Korean and Japanese dramas... Hotel del Luna is the few Korean dramas that I saw which fit your description.