My facial hair cannot compete with that particular cohort, so presented,.
But, ignoring for now that I'm not sure that what you ask is so simple, I'd have said get into Assembler and perhaps even learn how to use debug (
probably still there in the latest version of Windows, although it's not LFN-aware in
any way up to XP) with the hex-pairs. Its a big ask, but you can poke and peek video memory, keyboard input, serial ports, etc, (assuming the OS doesn't mediate too destructively, and anti-viruses don't have a cow with your attempts.. But get yourself a good pre-Win95 DOS and you won't have those problems). The book I once learnt from[1] even got me writing my own bootloader to the HDD... But there's not really a market for yet another OS (well, BeOS started a few year later, but never got to be as mainstream as the Linux kernel).
Hmmm, an idea forms. PIC programming. Simple circuit board, simple processor. Right now I'd suggest PIC over Arduino over Raspberry Pi, (chucking those other two "basic" platforms in for reasons I can't easily exaplain) but the Arduino might substitute better. (The RP is 'the' thing at the moment, but as yet I've not tried that out, and don't know if there's the same electronics-level interfacing possible.)
Anyway, the idea is you get an idea of the electronics involved. Maybe not what's within the chips, but trying to work out how to feed a higher bandwidth of data into a chip than its input pins nominally allows is an educational experience.
If soldering irons are not your bag, and you've got as much information about the program-side part of the computer operation as you think you need, I can't
easily give you "how a chip works" help, but you might want to look at (and implement an interpreter for?) an actual
esolang interpreter. Learn the trials and tribulations of juggling a program from the
inside, and if you write it as a "hardware simulator", you're in!
[1] Forgotten a lot of it. Do
not ask me to dive straight back in.