How to remove broken bolt?

[WranglerGuy]

This bold broke inside the recessed nut (not sure what to call this). As you can see there isn't enough meat to grab it on one side and the other is obviously inside. Any idea how I can get this out so I can use a new bolt?

 

[WranglerGuy]

Bottom photo is where the bolt should be going through.

 

[Randy]

You might drill smaller hole into bottom part and put screw into it

 

[WandereR]

You might drill smaller hole into bottom part and put screw into it

Huh? How would that work?