allan jenkins,
I've removed a few wheel bolts that had snapped of like this,; I believe somebody has already said the method:
Drill straight through, i'd start with a 6mm bit.
Use incrementally bigger bits.
If you have or if you can buy a good quality left hand bit.. about 8-9mm thick that might just get it out.
The hardest part is to make sure you get the first hole as close to the center as possible... do not hurry, use a punch.. try to drill... if it's not centered punch again to move the hole.
If you don't have a good left hand drill bit , you can just go to about 9-9.5 mm hole, and then use a hammer and punch to cave-in the walls of the stud.. they will most likely break off... really easy to remove at that point.
What brake disks are those?
I'm thinking of getting some MTec ones for the front... they seem similar to yours.