I once read a suggestion about removing a broken stud by welding a nut to the piece sticking up and then turning the
nut to get the stud out. On an assembled engine, doing anything like welding or drilling is a risk.

If you drill, the pilot hole needs to be exactly centered since as you go bigger on the drill, you will hit the head material if you start off center. Also, an EZout probably wont work since they are made to back screws out....not press fits.

Best way is to remove head, take head to a machine shop with a mill that can drill a true hole.

By the way, you are replacing all the studs, arent you?