Just take out the broken bolt, the easy out will come out with it
I have had pretty good luck with a air engraving tool. soak the stud with Aero Kroil first. the vibration from the engraver help loosen crud. it a step up from sitting there banging on a center punch to get the broken bolt to start backing out.
Also if you can heat that broken easy out up cherry red you can drill through it with a good bit while it is still glowing. a left handed Cobalt is what I would try if you can go this route. We use to do this to drill a hole in drill chuck keys so you could put a chain through them and wrap em up around the chuck when you forget to take them out.