Never ever try to remove a broken stud with an ez out. It will break off in the block nearly every time and make matters worse.
EXACTLY... If the stud was stuck enough to break... trying to turn it with an EZ-Out isn't going to work. Those are for stuff that isn't rusted in place.
Heating the stud cherry red will break the rust bonds, and allow the stud to be backed out. Just get it HOT... and it will generally back out. HOT, as in orange/cherry red!!! A basic propane torch will NOT do the job!
Welding a nut to the broken stud can accomplish this task. The heat from welding breaks these bonds, then the nut allows it to be backed out. When trying to do this, crank the welder up HOT, and try to put a lot of heat into it. Since a TIG isn't piling up a bunch of added metal like a MIG would, it allows you more time to put HEAT into the stud... making it more effective.
Stuff to know BEFORE trying to remove the studs:
If you have studs that need removed... and the head is off where you can get to the stud/block interface... use an oxy-acetylene torch to heat the base of the stud RED HOT... BEFORE trying to remove it. 99.9% of them WILL easily back out without breaking.
If you break one off flush with the deck... Use the torch to heat the stud up RED HOT... BEFORE trying to weld to it with a MIG. This will break the rust bonds AND make it easier to weld to. The heat will also 'crutch' the welder, if you do it while it's still hot, as it won't heat sink as bad. A propane torch can even help with this.
If you have a TIG to weld the nut with, you can probably skip the torch step, as it can add enough heat to break the rust bonds all by itself.
Good Luck!