I see people recommend EZ-Outs (or bolt extractors) frequently, but my personal experience with them is very poor; a success rate of maybe 5%.
And the thing is, when you try the EZ-Out route and it breaks, you have significantly compounded the problem because instead of a relatively soft bolt (easily drill-able) you now have a much harder EZ-Out (non-drillable) to remove. Your options now are very limited.
My first suggestion would be to weld a nut onto the broken bolt. I would then use penetrating oil (and be patient and let it penetrate - that may mean multiple applications over a few days).
Then when you're ready put a wrench on the welded-on nut. I would recommend trying to loosen it first, but if it doesn't cooperate, you might try tightening it and then trying back and forth as you slowly work the bolt out. If you break the weld, not a problem, get another nut and try again. You can combine the welded-nut technique with heating the area around the broken bolt.
If after multiple attempts the bolt just won't come out, you can still drill out the bolt and hopefully chase the threads. Failing that, you can drill out the bolt oversize and put in a Heli-Coil.
And the thing is, when you try the EZ-Out route and it breaks, you have significantly compounded the problem because instead of a relatively soft bolt (easily drill-able) you now have a much harder EZ-Out (non-drillable) to remove. Your options now are very limited.
My first suggestion would be to weld a nut onto the broken bolt. I would then use penetrating oil (and be patient and let it penetrate - that may mean multiple applications over a few days).
Then when you're ready put a wrench on the welded-on nut. I would recommend trying to loosen it first, but if it doesn't cooperate, you might try tightening it and then trying back and forth as you slowly work the bolt out. If you break the weld, not a problem, get another nut and try again. You can combine the welded-nut technique with heating the area around the broken bolt.
If after multiple attempts the bolt just won't come out, you can still drill out the bolt and hopefully chase the threads. Failing that, you can drill out the bolt oversize and put in a Heli-Coil.