Mac mini (Mid 2011) randomly reboots, but not while I'm using it
This ended up being a software issue. A clean install of the OS fixed the issue. I could not get the recovery partition to boot, so I had to use another Mac to create a bootable USB installer for macOS (downloaded from the App Store).  

Worth noting, I was able to put all my apps and settings back into place via Migration Assistant, BUT only after booting into macOS (not on first boot during setup where it prompts for Migration Assistant - it failed there for some reason).