The answer I think your digging for is what is the least amount of logic gates required to build a turing complete device.
Atleast that is the most I can minimalise "computer" to, anything less would not be able to compute everything.
Now that is all fine and dandy, but unless you give a task your trying to accomplish, It probably will not end up how you hope, e.g. the MOV command is turing complete, so if you build a very stripped back 8 bit cpu with an instruction pointer, some memory and only processes "MOV" from 1 location to another, you have a computer, It will be a pain to program or use. but it will be about as reduced as you can make it.
If you wanted to go on the other side of the argument, take a CPU design you like, e.g. a normal 8 bit, spend some time learning the tools universities use for old silicon processes. e.g. 10 um silicon, and draw it up and get it produced, congrats, you now have a CPU that is less than a square mm,
Or the third side, if you want out of silicon, you can build logic gates mechanically, you can likely use MEMs tech to build a mechanical cpu of your choosing down in the um to nm scale, definatly not a microcontroller, but a CPU none the less
Or even weirder, photonics, Its not outside of what is possible today to build an optical computer around the same scales, most of the logic gate designs are well documented. just I imagine it would use a lot more power maintaining something like 8 bits worth of memory.