Given 1 recording of my voice, how can I process it to sound like 2 independent recordings of my voice played in unison?
To make it sound natural you typically introduce some small random pitch, speed &amp; gain modulations. That's not a trivial amount of work, especially if you want something that sounds natural and good and maintains the original phrasing. 

This is a pretty common plug-in in audio processing. It's typically called "vocal doubler" or "voice doubler" and there are many off-the-shelf options available. Here is an example: https://www.izotope.com/en/products/vocal-doubler.html. No endorsement or commercial interest, but you can't beat the price :-)