The moon shone on his face as he spoke, and the girl was pleased to watch it, it seemed to breathe such an innocent and old-world kindness of disposition, yet with something high too, as of a well-founded self-content.
This is a complicated sentence but we can remove a few of the clauses in order to get at "as of" more directly:
The moon shone on his face as he spoke [and] it seemed to breathe such an innocent and old-world kindness of disposition, yet with something high too, as of a well-founded self-content.
It seemed to breathe such an innocent and old-world kindness of disposition, yet with something high too, as of a well-founded self-content.
It seemed to breathe such a kindness of disposition, yet with something high too, as of a well-founded self-content.
Whether we can trim out "yet with something high too" is debatable so we'll leave it in. "It" in this sentence could be either "the moon" or "his face" but you would need more context from the story to know exactly which it was. Fortunately, we don't need these details to understand "as of".
Rewording and rearranging lets us avoid the commas:
It seemed to breathe a [disposition that was kind], yet with something high too, as of a well-founded self-content.
It seemed to breathe a disposition that was kind [and was with something high], as of a well-founded self-content.
It seemed to breathe a disposition that was kind and was with something high, as of a well-founded self-content.
Therefore, "as of" means either (1) "similar to" or (2) "like it was coming from":
It seemed to breathe a disposition that was kind and was with something high, [similar to] a well-founded self-content.
It seemed to breathe a disposition that was kind and was with something high, [like it was coming from] a well-founded self-content.
Based on the little context we have been provided, I would guess that (2) is most likely and a possible rewording:
His disposition was kind, yet with something high, and suggested that he possessed a well-founded self-content.