Maybe better to choose a particular hard problem that is interesting and focus on that. Something that would be neat to do but isn't as simple as just calling a few library functions.
Start with a course on computer architecture / digital design. Something that'll have you put together a simple 8 bit CPU. Move your way up with a course on operating systems - processes, swapping, cache invalidation, file systems, drivers.
Then, maybe something on compilers? Or how to write your own interpreter.
Finally, a good networking course is pretty important.
Very little of this is theoretical compsci, but it's something that will get covered in a degree program. That said, knowing how to recognize what kind of class of algorithm we're looking at, and data structures all around.
It also depends upon what you consider to be a deep level?
Are you interested in electronics and signal processing, mathematics or the structure/design of programming languages? Are you interested in individual computers or distributed systems? Are you just interested in computers or are you interested in using computers to model other things, like economics, physics or virtual worlds?
At a minimum you could brush up on algorithm / data structure understanding and some of the math behind that. Problem is that as soon you gain understanding of something it will simply expose you to deeper subjects that you don't fully understand. You will never reach the bottom of all of these rabbit holes.
Ultimately it depends on where you see your shortcomings that are preventing you from doing what you want. Do you wish you had better credentials so that you could get a job with better pay or more interesting work? Or do you find yourself frustrated because you are not able to sufficiently grok a certain subject area.
You will learn everything from logic gates/transistors to software.