Because the nipple is obviously hard (or it wouldn't have broken), and it has a Very small hole in it, an E Z out may be difficult to get in such a small size.
Drilling the hardened steel will not be easy and if you use a standard type drill bit, the torque from drilling will tend to tighten the nipple even tighter.
If you can find a "Left Hand drill bit" that would be the way to start this process. (see this link)
http://www.hi-line.com/industrial-supplies/left-handed-drill-bits/
I haven't done business with any of these suppliers but they might be worth a thought
http://www.cvfsupplycompany.com/drbi13pcleha.html
http://www.thefind.com/hardware/info-15-piece-hss-drill-bit#page=1
http://www.wikio.com/product/power-drill-bits-reviews-12064-page1-sort0.html?x=6&y=5&gk=left+hand
If you didn't read the links, a Left Hand drill bit turns the opposite direction from a normal Right hand bit.
That means you will have to run the drill backwards but most modern electric drills can do this.
Running backwards makes the bit try to unscrew the bolt or in this case, whats left of the nipple.
Often this will unscrew the broken off piece all by itself.
Use a 1/8 inch up to a 3/16 inch diameter drill bit. This will not damage the existing threads because it is slightly smaller than they are.
If the piece of the nipple doesn't dislodge and unscrew a E Z Out may be needed but it will at least have a hole that is large enough to allow it to have the strength to remove the broken piece.
Before you go ordering something on the Web, give your local hardware store a call.
They may have a 3/16 inch Left Hand drill bit in stock and that would certainly be cheaper than dealing with orders on the Web.
Another way of removing the broken nipple requires a Dremal or equal high speed tool.
Using a thin "cut off wheel" on the 1/8 inch arbor you would cut a screw driver slot into the exposed end of the broken nipple. Then, using a good screw driver that fits the slot you would unscrew the piece.
If you don't have a Dremal (or equal) this is a pretty expensive way to go because they aren't cheap and the little grinding wheels, cut off wheels and burrs are quite expensive.
Because you said you hadn't applied any real torque to the nipple, a pointed center punch might do the job as well.
To use it you would place the pointed tip almost out to the edge of the screw thread on the broken nipple.
Lean it backwards slightly so that when it is struck with a hammer it will drive the nipple piece in a counter clockwise direction.
Then, tap it with a small hammer or mallet.
If your lucky the nipple will turn slightly.
By changing the angle of attack a bit and continued tapping you might be able to unscrew the piece.
Good Luck.