Better than an easy out, which is square and has to be punded into the hole, is the reverse threaded and hardened screws they sell for this application. Get one about half the diameter of the stub along with a good drill bit that same diameter as the reverse threaded screw. Drill a hole as close to the center of the stub as possible and screw the reverse threaded screw into the hole, when it comes tight it will back the stub out.
What material is the screw made from and what material is it lodged in?
If you broke it trying to take it out it's seized. The first step is the penetrating oil. Let it soak as long as possible.
Is it broken off flush with the surface?
The screw broke while i was tightening it, wasnt using much force at all. Not sure on the material, its whatever Penn uses for the anti reverse components(underneath the rotor) on their SS series. Its not flush with the surface.
Never saw a set of easyouts that were square but Im sure they exist. The ones Ive seen are like big reverse threaded screws. It may be difficult to find a screw extractor that is small enough for the screw size that broke. You may also need to flatten the broken screw to get the drill bit to go straight. Be very careful not to drill sideways into the tapped hole or you will mess up the threads and the new screw will be difficult to get back in.
Is there enough material to grab onto with a pair of locking plyers? But don't twist away yet....try this before yah do the twisting deed: (Be careful if the material being threaded into is not metal or you might crack the material) Do you have a soldering iron or gun? Fourty five watt job ought to work ok but one of the more powerful Weller guns is super. Put the end of the iron on the top of the screw and put the heat to it. Now start dripping a bit of your favorit brand of rust buster. Cool it down (quickly if possible...freeze spray is cheap at Rat Shack) then hit it again with heat and oil. It'll come out of there. There is always the drilling it out method........Oh, if yah don't have a soldering iron then try a old screwdriver or butter knife. Heat it on the stovetop till the end gets cherry then touch it to the screw head.
To agree with what Mike said, drilling will work, but even better if you can find a left hand drill bit a little less than half the diameter of the screw, and a reversible drill, you can begin drilling down thru the screw, and more times than not the drill bit will reach a point where it just backs the screw right out.....penetrating oil is a good idea as well.