Come to think of it, I used both stud extractor and EZ out extactors yesterday.
IMHO & FWIW the following is a litany of what I did. I had a weight assembly break off a tractor and had three bolts, one sheared flush, one out a half inch, and one out about three inches (18mm bolts). First- apply PB Blaster, I just always do this.

For the three-inch broken bolt shaft I used the Sears cam type stud remover, as it required a lot of force and a long 1/2 inch ratchet handle. It came loose grudgingly.
But the half-incher was too short for the stud remover.

For the half-inch bolt threads sticking out, I hit the end of the remaining threaded shank with a hammer, more PB Blaster and then used a straight jaw large vise grip tightened onto the threads before locking, then locking and crushing the showing threads. It came fairly easy. Another post said cut a flat which helps if the vise-grip slips. Welding a nut on also works as it heats and grips both, but is more of a pain and usually more useful on only larger shafts and all exposed studs if you have a welder handy.

Prior to saying the below, I echo the warning on extractors, if it does not back out the bolt easy, don't force as it will be harder to get out the hardened extractor or EZout. Also when drilling, keep square as broken drill bits are as hard to get out as broken extractors.

For the flush mount, I first tried the center punch and cold chisel to drive it out by trying to turn it ccw. Didn't break loose, so I went for the screw/bolt extractors things that look like a tapered tap with big spiral threads going the wrong way. FYI, I was taught bolt EZouts are tapered square bits with one cutting edge on one of the four corners although some techs interchange the terms. I first selected a drill size about 1/2 the diameter of the broken bolt shank and carefully center punched the exact center of the hole. You can do this by successive hits with the center punch angled to point in the direction you need the hole center to move. I tried inserting the extractor that would go about halfway in and turning, but the thread did not give, so I heated all around the broken bolt with a torch and tried again, still did not give, so I upped the size of the hole to about 3/4 the bolt diameter and pumped PB Blaster through the hole to the back side as this was a blind hole. I then inserted a yet larger extractor and tried, this time the thread turned and I have a threaded cylinder I removed. Success before the next step.

Had it not come, the next step would be slowly creep in drill size until I could see a thread peeking through the bolt shaft, then use the cold chisel to collapse it inward until I could remove it with a needle-nose plier. An extractor cannot be used after a certain point as the bolt shank gets too weak and you distort and wedge the threads, why I stop at 3/4ths the diameter.

If you go more than a thread showing or are off-center, you need to replace the thread with a helicoil, BTDT only once!

As a rule, I always chase the threads with a tap and blow out the hole to clean it. And I alway use anti-sieze on the new bolt threads. After all, it may fail again and I want it to be EZ out next time.