I agree with the EZ-Out avoidance advice above. I was taught that an EZ-Out was only for removing a bolt that broke while tightening. Never for stuck bolts that broke while being removed. I ignored that teaching only to learn that broken bolts with broken EZ-Outs in them are much much harder to remove than the bolt alone.
Before breaking flush = Patience, heat, & penetrant with time to soak. Work the bolt back & forth with gentle force, more penetrant, & more time to soak. Vise Grips if there's a broken nub to grab.
After breaking flush = Punch, drill, & tap.
I have heard of guys welding a nut onto the broken bolt in that situation, but haven't tried it myself.