@Juniko It doesn't seem like you watch Thai dramas, but I'm still putting it out here:
Tawipob was the first thing which came to my mind. I thought it seems very fitting of your request !! Fem lead takes a HELL LOT of initiative (all without being annoying) while the male lead is passive and conservative, but quite obviously mutual in feeling - it is super adorable.
Other dramas which I can think of, may or may not fit, but I thought might fulfill that feeling - or someone else might find these of interest:
Kahogo no Kahoko (jdrama)
Go Princess Go (cdrama): fem lead is technically possessed by a guy but at least you get to see her being the one getting really enthusiastic over male lead. not to be taken seriously, the crack is quality if anything.
The Fox's Summer (cdrama): fem lead initiates a lot of things in a romantic relationship which are traditionally expected to be done by men (eg. proposal) - male lead is really precious - relatively shy and adorable - but the drama and story on the overall was a drag (especially the second season which was a pain to watch). nevertheless, I still loved the fem lead for taking initiative - absolutely worth mentioning. but only if you're really bored and want to waste time on an average romcom, this is your thing.
Ban Shu Legend (cdrama): still don't think there are Eng subs for this but if anybody understands Chinese and is interested. I enjoyed this one.
I love this trope too - would love to hear everyone else's recommendations !!!