So when a Brake Bleeder breaks off...

Little warning on the ez-out.

If the bleeder is so siezed in there that you broke it trying to remove it, chances are you’re simply going to break the ez-out as well. The ez-out, by design, has to be smaller in diameter than the thing you’re trying to back out. And once you snap that hardened steel ez-out off in there it will be a huge PITA to drill out since ez-outs are generally as hard or harder than most drill bits.

Get yourself some Kroil, the best penatrating oil I’ve ever used:
http://www.kanolabs.com/
Spray that on, let it set for a day. Then try the ez out. If it doesn’t feel like it’s going to come, give up. Drill it out oversized and put one of those oversized bleeder repair things in there.