It seems that this trope was trending a decade ago. So there will be many older dramas in my list.
I second the Secret Garden recommendation, that was the first that came to my mind.
Bridges of Love but settles for being (semi spoiler:) her friend for a while (while still pining for her). Really obsessed hero.
Something about 1 Percent
The Master's Sun
The Greatest Love I'm not sure he quite offers her to be his mistress, but he feels like he's too good for her anyway.
My Lovely Sam Soon Very much like Secret Garden (the couple dynamic)
Dreaming of a Freaking Fairytale I'm not sure about this one because I've not seen it yet. But it seems like it.
The Beauty Inside this one is more egalitarian, as they're both on the same wavelength as to where their relationship stand.
Cruel Romance This one is high angst with (semi spoiler:) many people dying by the end.