Steven Universe. The first handful of episodes, Steven is just a child (and a borderline annoying one at that). Always yelling, running around, goofing off, and even making childish mistakes that his guardians, the Crystal Gems, need to step in and fix.
But as the show continues, Steven matures mentally (and a little bit physically, if you watch the movie and the short sequel series, Steven Universe Future), and by the end of the series, pretty much everyone is turning to him for wisdom and advice, even his own guardians.
The Crystal Gems see an enemy and their instinct is to fight. Steven sees a misunderstood living person and wants to communicate. Throughout the whole series, he shows that it's better to talk out your problems instead of engaging in battle. His summoned magical weapon is a shield and he uses it to protect friends - and foes - as he tries to resolve problems his own unique way.
And the lesson isn't crammed down your throat either; it's subtle in how it's introduced. At first, you just see Steven as young and naive. Choosing friendship and kindness because he doesn't understand the serious threat. But over time, you start to realize he's actually onto something, and his methods actually have merit.
There's also some deep lore hidden in the show that slowly presents itself as the series goes on. The plot sounds simple at first, but then you learn of a great war that took place between Gems that isolated the Crystal Gems on Earth. And Steven's mother had a crucial role to play, with her own hidden past that Steven pursues in order to better understand himself.
Steven is also constantly at war with his own ideals, as everyone else just wants to fight and encourages him to do the same. He has to struggle with his own moral code and decide if violence can ever truly be an answer.
My wife and I just thought it was a cute kids show and idly watched it during a quiet evening. But we got hooked, and by the end of the series, we were crying. It was a very emotional and dramatic (and fun) series that taught good communication and respect for others.