I don't know if you broke a reverse spiral easy out, or the type with 4 straight flutes. If it was the straight flute type, there is a 4-legged tool to try to pull them back out. I've never used one, and to me it just looks like a way to break another tool off in the hole.

The suggestion to weld a nut onto the remaining stud is a time honored method, though having two metals in the hole may make a good weld tough.

Another method (provided the stud is broken off in iron and not in aluminum) is to blow the broken off stud out with an oxy-acetylene cutting torch. I have never tried this when a broken easy out is involved. I suppose it is possible that it would blow out the easy out and leave the stud, but that would be an improvement since you could then drill the stud.

If you are blowing a stud or bolt out with a torch, you only get one chance to do it, so make sure it is plenty hot when you pull the oxygen trigger because you have to blow it all out in a single pass. If you blow half of it out, you can not get enough heat down in the hole to melt the second half without over heating the surrounding threads in the cast iron. After the stud is blown out, clean up the threads with a tap.

Typically I only use the torch method when space limits won't allow the use of a drill, and thus it may save pulling a head or the whole engine. But, in your case, it may be worth considering since the broken easy out is a problem to drill.

For what it's worth in the future, I would not recommend an easy out for an old stubborn stud or bolt. They work okay if you snap something off while you are installing it because everything is fresh. They may work on an old broken part if you put a torch to it first. But, other than that, the easy out will usually break.

Charley