Broken extractor is most likely as hard as a standard twist drill.I'm going to try drilling everything out and repair with a helicoil insert.
Do you have a MIG or TIG welder?
I would weld a flat washer to the top of the broken mess down in that hole then weld a large nut to the flat washer, let cool slightly and use a wrench to remove the broken bolt. Might take several tries and at worst you'll soften the extractor so you can drill it out if needed.