D'oh, not fun. I'd grind the broken ends smooth with the flange. Remove backing plate and you may have a little stub of bolt to grip with vice grips or a pipe wrench.
IF that doesn't work, center-punch the grind and drill for the correct size ez-out. If that doesn't work, you may be able to put a small pipe wrench on the 1/2" of stud, and screw it out the back. If that doesn't work, you may have to carefully drill it out, and re-tap with the correct size thread tap.
Hope that rear end has c-clip axles, cuz then at least you could get the axles out to access the damage better.
good luck
chip
