With a good background in physics and chemistry, I want to learn about modern chips and electronics, which is often on a much smaller scale and more chemistry and quantum mechanics than soldering.
It depends what you want to do, but the standard way we went through was chemistry and physics, then some more atomic/nuclear physics and mineral and organic chemistry, then solid state, then circuits, control theory, measure theory, etc.
You can look into MIT's EE curriculum on opencourseware, but it's a bit too light.
If I don’t want to get a job, why the hell would I pay for the university courses when I could follow their curriculum, books, etc. in combination with things like MIT OCW. Assuming that I’m the sort of person who can keep on top of that sort of autodidactism.
I mean I suppose yeah there’s a lot of stuff you can’t do on your own (I imagine VLSI is out of the question), but you can get your hands on FPGA dev boards, etc. That seems to be good enough for designing custom hardware as a hobbyist, along with playing with discrete components.