Barazinbar just seems to have a nature of its own. One special mountain. I always left it as that in my mind. A stone with a personality.
We can't say that anyone in particular "shaped" it and left a trce of their spirit inside, because Caradhrass is said to dislike both Elves and Dwarves, and Men weren't that lucky either. Even a wizard did not pass. And where the strong failed, even the hobbits failed.
But why specifically Caradhras? I understand that it was done for the purposes of the story, but why not other mountains as well?