Imperial Doctress is the first one that comes to mind. I Hear Your Voice fits too I think. Witch's Romance, more or less (she goes on some blind dates and her ex-fiancee shows up out of the blue at one point). The King's Woman in some respects, but maybe not really the dynamic you're looking for (he basically holds her hostage and tries / somewhat succeeds in making her fall for him / not really her emotional support). In Empress Ki, the dynamic is a bit like the King's Woman, and you could even say your criteria sort of applies to both romantic leads in different ways.
In all of these (except maybe Empress Ki where male lead A loves her first but has to watch her marry male lead B, but later finds out she had his kid and still loves him but also male lead B knows that she loves male lead A for most of the drama, but she marries him and sort of falls for him later on - its complicated), the girl is aware that the guy has feelings for her, in most cases from very early on, but doesn't fall for him until much later even though they are still close / she relies on him for support in certain circumstances.
Also, Healer sort of has this dynamic, except the male lead is both roles? (his undercover / clark kent persona is the emotional support guy who has to watch her have feelings for someone else and his night courrier identity is the guy she first has feelings for).
