If you come across a broken head stud in your water boxer engine, the process to replace is as follows:
1) Remove engine, completely disassemble, clean block thoroughly
2) Heat engine block to 500 degrees
3) Pour penetrating wax into the threads
4) Grab whatever part of stud you can, and try to spin it out.
If that does not work (about a 50/50 proposition), continue as follows:
5) Build an appropriate fixture
6) Using a milling machine and special, extra-long tooling to get down to the bottom of the water jacket, mill the broken stud perfectly flat and flush with the engine block
7) Using special, extra-long drills, spot center-drill, and step-up sizes until you are just touching aluminum
If you cannot get the remainder of the steel stud threads out of the aluminum block threads (about a 50/50 proposition), continue as follows:
8) Drill the hole to a larger size.
9) Using special, extra-long tooling, tap hole and insert a thread repair insert
Note: If during this process you accidentally drill off-center, the repair might require thread repairs and/or welding and/or discarding the block and starting over.
I could write quite a more elaborate article that this, but you get the picture. If the thing does not come out easily (they never do), or is broken off flush at the bottom of the water jacket and there is nothing to grab to even try and remove it: There is nothing I can tell you or sell you to get it out. It requires and LOTS of tools, patience, experience, and sometimes another engine block.
So, that $50/stud, $500 worse case engine core charge we collect doesn’t sound so bad anymore, huh?