Homemade Broken Screw Removal Punches

I used to be a machinist at a Ford Truck dealership and we would get cylinder heads in the machine shop where mechanics had used and air wrench on the exhaust manifold studs which resulted in breaking the studs off even with the cylinder head. The easiest way to get those studs out was to hold a cutting torch on the stud until it was nearly white hot. Once that was the case, just a touch on the handle that delivered extra oxygen ,normally used for cutting, would blow out the stud and leave a clean hole to run a tap in to clean it up. The studs had been located in a place where there was a lot of heat and they were all but welded in to the cylinder head. I did use punches like you show to begin with and it would take a lot of time to drill a hole in the middle of the stud and increase the drill size until you reached the root of the threads then pick the rest out with a punch like you are showing. The punches work for sure but there are other ways to get a broken bolt out just like there are more than on way to skin a cat.