If possible welding a spot on the fastener as suggested by Grigg or even better welding a nut onto it should be the first choice. Drills, taps, and easy outs/extractors are generally made of high speed steel which is not as readily weldable and difficult to remove without carbide tools which is where EDM can prevent furthur damage. Another benefit of EDM is that broken fasteners are removed with no destruction of the parent material/thread and so should be a first choice in applications where a helicoil or weld repair is unacceptable.
