I would suggest:The greatest love

I think you will like it,Male lead falls first chases female lead whereas female lead rejected him twice,  I think female lead is his first love as he never felt like that before. I wouldn't say he is cold but he is kinda proud. Give it a try :)

  • XX
  • The Producers
  • Dating Class (female isn't the lead)
  • What's Wrong With Secretary Kim
  • Go Go Squid
  • 1% of Something (Something About 1 Percent)
  • Thirty but Seventeen
  • My Husband in Law
  • Mr. Honesty
  • My secret romance
  • Clean with Passion for Now
  • Touch your Heart
  • A Love so Beautiful
  • Playfull Kiss
  • It's Okay to Not Be Okay
  • It's okay, that's love
  • Meteor Garden

I think My Little Happiness has this trope. He starts chasing her VERY early on! 

 SSKF:

It has cheating but Jao Sao Rim Tang.

Let me explain the cheating:
He was a big player, using women who offered, only for sex never believing he will fall in love. Then he has to get married for a reason. He is rich and handosme and anyone would marry him but he only wants FL. He cheats a couple times when women throw themselves at him. But weirdly, he always comes back to her and even tells his bed mates, while in bed, that his wife is fascinating and fabulous. Then he wants to sign the marriage certificate with her, to make it legal. He stops cheating after that, when the marriage became real for him and he realised he was learning to love one person.

PLEASE NEVER RECCOMEND THIS DRAMA TO ANYONE EVER EWW

I GOT DIARRHEA BYE-

Oath of Love, he is awkward, but very smitten, and she doesn't have it on her radar at all. 

More dramatic, recently asked Love Between Fairy and Devil, which otherwise has all the things you asked for. 

Once We Get Married, also cutesy and cliche, but he also has never loved and will never... Ooooh, contract marriage.

The legends is amazing for this ...as well as romance is a bonus book ..ancient love poetry ...lady and liar...before we get married....honestly I wish there were more good shows in this genre.

The romance of tiger and rose!

Please keep recommending more dramas like this

 0330dramalove:

High End crush -it's short and cute show

I agree this drama was so cute 

I think you would enjoy The Starry Love. Both ML and FL fit your bill. He lives for her and is a complete greenflag. She's rebellious and spunky + speaks her mind. I really love this drama one of the best.

I need more dramas like this please more dramas

Here's a list I made for head over heels MLs, I note where they chase for a long time while the FL is oblivious: https://mydramalist.com/list/3rkQqyP4