hi!
I'm currently watching a taiwanese drama called ToGetHer with Jiro Wang and Rainie Yang, and I think it could fit what you like. Although their relationship starts with the typical bickering, very early on you can feel how much more caring and gentle the male lead is with the female lead than with other people - and of course, this just grows with each episode. There are so many moments in the drama where he helps her, pays attention to her when everyone else forgets her (she's a quiet girl that has been forgotten all her life by others), tolerates how bizarre she can be (she's obsessed with a manga character, yet he doesn't mock her or try to change her, but on the contrary tries to adapt himself to her world), treats her to something special, cares for her when she's ill, saves her... (it's not one-sided though, she definitely does just as much for him).
I'm only halfway though, but I'm loving this drama :)
Good luck!