Where can someone go from "knowing the basics" of design, to mastering the principles of design?
If you mean UX design, here are a few spots
This is a great place: https://aycl.uie.com/
All have great books on a diverse set of UX and design topics.
Workshops and conferences are useful too, but they can get very expensive fast.
I am a member of https://www.interaction-design.org/ It is not free but very insightful. There are courses and literature and also a community of designers.
Start looking at High Resolution's videos on YouTube with the most inspiring Design leaders today. After you watch the 10 episodes (11 by the time you read this) you will notice a pattern: everyone has integrated Design Thinking into their process.
So you should learn that. The best way is to read Don Norman's book and follow these free courses next month by IDEO - read every word of this website and subscribe to their courses: http://www.designkit.org/.
You'll see most designers from HR (like Facebook's head of design for example) are ex-IDEO employees. And that's for the reason above.
Do this stuff, then build some products with this process in mind and you can get any design job.
Even Apple has this approach and you can learn a lot from them too: https://developer.apple.com/videos/design/