I don't know the name of the trope but I'm a sucker for burly, big, scary men (and women) finding in their icy hearts room for an orphan child they've saved.
Like, the guy slays monsters or does jobs for the shady underworld. One day he crosses paths with a pathetic, vulnerable and abandoned child/ youth/ thing and he's ready to leave them to die but that day something prevents him from doing that. And he saves them, and he's gruffy and mean at first cos it's all new to him. He's not used to showing his softer side - he's forgotten he even had one. And they bond 🥰 both learning from each other and giving the other strength and eventually love. Then something horrible happens and his ward is in danger! But damnit he would rampage through hell to make sure his child was safe because he's a daddy now
It's too much for me. I love that they have a family bond that's not based on blood but it might as well be because it's just as strong.