Jerk with a Heart of Gold/Fan Works

He knew Ryo was just trying to be a friend... a crazy, narcissist, extremely annoying friend, but a friend, after all.

In this Death Note fanfic, Matt is easily the most notable example of this trope:

Matt: A good friend gives you a shoulder to cry on. A great friend gives you a kick in the pants.

Fluttercruel from the Pony POV Series became this under Fluttershy's care. She's still a Jerkass, sure, but she shows her heart of gold by forcing herself to the surface to help calm Rainbow Dash down of her own accord among other things. Worth even more note is that in the Bad Future we're originally shown, Fluttercruel was a Complete Monster who did such horrible things that Twilight Tragedy refuses to tell us.
- Firefly from Ace Combat: The Equestrian War, most definitely. There are times she acts really cold toward other ponies, especially Fluttershy at the beginning (going as far as to slap her!), as well as Derpy and Medley later on. But deep inside, she's just a troubled mare, trying to readjust herself to the circumstances around her. Rainbow Dash is there to help her.
Mello and Light in The End Is Near - there is Mello's Pet the Dog moment or rather, "Beat The Dog That Goes After Near With A Cricket Bat Until It Stops Moving" and then there is how Light verbally crushes the snobby stewardess who tries to make L sit properly. He's petting one dog while kicking another....
In Legend of link:lucky number 13 Ganondorf shows shades of this. Mainly towards his daughter Separuu. He even goes so far as to sacrifice his own soul to save the one his daughter loves, which is the one he hates the most, Link .