This is a problem that is all too common, since some recent replacement parts have been sub-standard. If you have seen "The Nature of Threaded Studs" you know that double threaded studs should be installed finger tight only, and tightening a free-spinning nut does not screw the base thread in any farther. When a stud breaks it commonly breaks at the top of the base thread where the root diameter of the coarse thread is slightly smaller than the fine thread on top. In the case of the cylinder head, you probably have to remove the head for access to the broken stud. Otherwise removal of the broken stub end should be no problem, as the thread should still be just finger tight.

Use a center punch and a light hammer. Place the punch off center near one side of the broken stud, and make a shallow prick mark. Tilt the pinch to one side and tap gently to rotate the stud anti-clockwise to unscrew. Once it is up a couple of turns you can unscrew it with pliers.