Well, Studio Arms Elfen Lied attempted to tackle this very question with their adaptation of the light novel, Aesthetica of a Rogue Hero. With a rather unique premise as a backbone, I was very curious to see what this series was about. Unfortunately, what followed was a lewd, generic insult to anime fans everywhere, with more breast development than character development. The story sounds promising from the start. It begins with our conceited, overpowered protagonist Akatsuki leaving a foreign land to which he was summoned to defeat an evil Dark Lord.
He flees through a forest pursued by warrior maids whom he defeats by stealing their underwear. Upon returning home it is revealed he has brought with him Miu, the Dark Lord's daughter who was entrusted to him by her father with his dying wish. Together they attend entrance exams for a special school where they both prove to be extraordinarily gifted in combat based magic. Akatsuki has an encounter with student council president Kyoya Hikami. They both enroll in a special school for people who have returned from other worlds with magic powers. Akatsuki immediately get into trouble by beating up the class bully Onizuka, earning him the attention of the school's Discipline Committee, especially student council Vice President, Haruka Nagase, whom Akatsuki deliberately aggravates by managing to steal her underwear. After beating him up the three girls shower together and end up becoming friends via their new mutual dislike for Akatsuki, leaving Miu to wonder if Akatsuki made himself the bad guy on purpose so she could make friends.
Akatsuki came back to his world after defeating the Demon King and becoming the "Rouge hero" in the alternate world of Alayzard. He was entrusted by the Demon King with his daughter, Myuu whom Akatsuki brought back with him. He is usually very laid back and filled with confidence.
The story only picked up and showed the depth of the characters after the revelations in volume 5. This is common in the fantasy genre that needs time for world building and time to slowly build backstory. Seriously, I think the anime was only the beginning arc of the story LN volumes Its no surprise that the manga that barely covers volume 1 cannot show enough depth.