1. There is to be a romance between the main   characters.

2. It would be best if there was a misunderstanding at the beginning and there was a Hate-Love relationship

3. ML look older (as an actor) than FL or just be a few years older in drama than FL ( as an character)

4. It would be nice if his character was so cold

There are a lot of dramas of this type that I have definitely watched, but right now, while writing, "Memories of Alhambra" came to my mind as an example

The King's Daughter, Soo Baek Hyang  if you are willing too put through the beginning, the rest of the drama is fire, and exactly what you describe

Chocolate

Your House Helper

Where Stars Land

Drinking Solo

Fated to Love You - it has everything you listed + great chemistry between the ML and the FL + the story flows nicely and I didn't get bored at all

Koi wa Tsuzuku yo Doko Made mo - apart from the missunderstanding part it has everything + the ML is really cold in the beginning and it's much older then the FL as well

Secret - this would be my first rec. The chemistry is insane and you can check all the boxes you mentioned

The Innocent Man - it has everything apart from "older ML" but I really encourage you to watch this one

Because it is my first life - ML is very cold! I love to see how they develop their relationship from a fake marriage to true love.

She was pretty - Park Seo Joon is not very mature looking but it meets all other criteria. And the second male lead is adorable!

Touch of heart - I could be bias because I’m a Lee Dong Wook fan!

About Time

Crash Landing On You

Her Private Life

Itaewon Class

The Beauty Inside