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The trick will be getting enough of a grip on it to pull it out. Once you get it out, installing a new one is no deal. If it was (or is) a screw-in stud, slap a wrench on it and turn left.
Screwed in has a hex at head surface. Pressed in is just a round piece of stud left. I am sure someone will know how to get it out if it is pressed. I have never had to do it. mds...
I would just go ahead and pull the head and take it to a machine shop. They would probably drill out the old stud and replace it with a screw in stud. I think trying to do this with limited tools at home would be a real headache. Unless of course you have the right tools and knew what you were doing along with patience and time to spare. Plus they could check the head to make sure there isn't any other damage that might have been caused by whatever broke the stud in the first place.
First, file the end of the stud smooth. Carefully center punch the stud in the center and drill through the stud with a tap drill for a 10-24 or 10-32 tap (I forget the size). Tap the hole in the stud. Get a fender puller/slide hammer and replace the sheet metal screw with a steel machine screw. Attach the fender puller to the stud and work it out with the slide hammer. If the stud won't move, then it is machine shop time. That is how I removed them back in the 70's when I did that sort of thing for a living.
Two things usually caused this. A bent push rod or the valve stem/rocker arm wear surfaces started wearing unevenly. The latter usualy required regrinding the valve stem or replacing the valve.
My friend had a Chevy 350 in a boat, the kind of setup where the water ran through the exhaust manifolds. He was running and lost power, after removing valve cover for him, the rocker stud was pulled out of the head. Long story short, the cooling jacket rusted through in the exh. manifold and water got back into the exhaust valve, the one rusted/seized up tight and when push rod came up to pivot rocker arm and the valve didn't move it leveraged the rocker stud out. We removed head and had a machine shop check it out and ultimately he had to get new exhaust manifolds also.
Something in your engine caused the stud to snap, that is not from normal wear. Just something to think about.
PS---Also be careful with the above method of drilling and removing with an EZ out. If that EZ out breaks off in the stud, you are F---ed, then you will have to remove head and haul it to a machine shop. JUST BE CAREFUL
You need to analyze the broken surface of the remaining stud to determine what caused it to fail. If you can post a photo of the broken stud surfaces, we can give you a 'read'. Basically, if those surfaces are very rough and jagged, it is likely an "instantaneous" fracture and there was some finite point of failure when it broke. That would indicate something else bound up and you need to locate the problem and fix it before you go back together. If the surface has only a small area that is jagged (where the stud finally snapped), but most of the surface has a 'smoothed-over' appearance, the part has been working a long time to fail and is probably a bad stud or it was damaged during installation and finally fatigued to point of failure...not likely to have another source for the failure. It's important to know which so that you can resolve the source of the high-stress condition.