Popping in to add another two cents - I see that someone’s already given the example of asking
「○○」知りますか? (do you know “○○”?)
which I think it very helpful for understanding 知る. A very common exchange you could have is
「○○」知りますか?
いい、知りません。 or いいえ、聞いたことはありません。
In contrast, if one of my students is confused during a class, the most common thing I’ll hear from them (other than ムズ, that is) is 「わからへん」 - or, in less 関西弁 terms, 「わからない」。
If I’m asking my students if they understand an explanation, I use 分かる - if I’m asking if they know a certain manga, I use 知る. If a teacher is explaining something to me and I have the lightbulb moment, it’s 分かった. If a teacher tells me a new fact and I’m surprised, it’s えええ、知らなかった!
To put it in one (English) word, the difference is between “knowing” and “understanding,” like some other folks have said. There’s definitely a learning curve of hearing it used natively though, and I still have times myself where I’m not sure if it’s better to use 分かる or 知る with students and coworkers.
But in the case of your original question, I honestly think that your initial thought of “What I understood about Miyazaki” is pretty decent - changing it to “learned” in English isn’t really because 分かる means “learn,” but more to reflect that it’s new information that you have come to understand, presumably through a reading or similar source.
Sorry if this is repeating info, just figured I’d toss another answer in the ring. 
Seconding!