Changing Default / Primary Monitor in Gnome 3

The proper way to do this is to run System Settings -> Display and drag the black bar at the top of your primary monitor to another monitor.  I find the Display interface really difficult to use and unresponsive.

So, as much fun as it is to try to get that UI to work, this is my work around using the CLI.

list all your monitors:

xrandr  

This will list the IDs of all your current monitors.  To set a different monitor as the default type something along these lines:

xrandr --output HDMI3 --primary

where HDMI3 is the ID of the monitor you want set as your primary monitor.