In both dramas the leads (and more characters) are connected by a past life. In Extraordinary You it's a "story" but it still counts as a past life since for the characters it was their life. In both cases it's revelead in later episodes that this other life exists and what happened in there and how it connects the leads and the other characters.
Also *spoiler* in both cases the FL forgets about the ML towards the end but the ML remains by her side anyway, trying to make her remember they were in love.

Same male lead (Taecyeon). The main leads meet and bicker a lot at first but end up falling in love. Each episode focuses on a specific story that unfolds a bigger plot. There is a comedic duo of boys that follow the main leads in all their adventures.

Depiction of women's issues in the Joseon Era, there's a lot of funny scenes but the drama's main plot has a more serious tone, main leads bicker and fight when they first meet but end up falling in love, people in high positions are corrupted and the main leads fight against them.