Not sure if this applies, hope it helps:
I've had good luck removing broken off steel bolts/studs using a MIG welder. How it's done depends upon how deep in the hole the broken part is and what material the broken part is threaded into. Aluminum castings make it a bit easier but this method can work with iron castings as well.
With aluminum castings the MIG wire is fed straight down into a recessed hole where it fuses to the broken stud/bolt using care not to hit the sides of the casting with the wire as the weld is performed. Using a series of short welds the stud bolt is built up to the surface or just above the casting where a washer slightly larger than the weld and a consumable nut is placed over the weld. The MIG welder is again employed to weld the built up weld to the nut and a wrench used to remove the broken part. It may take a couple of tries if the end of the broke part is dirty but it does work. The heat of the weld works on any corrosion to loosen the stud/bolt in the casting so it more easily unscrews.
In cast iron the same process is used but with a minor twist. A piece of thin copper is formed into a tubular shape small enough to fit down the hole before the welding is done. Since the weld will not stick to copper this protects the threads or smooth hole in the casting.
If the stud is broken off near the surface things get easier. The build up of the broken stud/bold is shorter or unnecessary. Get the end of the broken part as clean as possible (free of rust and oil). A thin washer to protect the surrounding area and a nut are applied as in the previous scenario, the nut is welded to the broken part and the broken part is unscrewed.
Of course the anything that might be harmed by heat nearby the operation should be removed first. In the case of a couple of broken bolts/studs holding some component (perhaps a head or jug) that can be removed by removing the remaining bolts/studs using conventional methods (wrenches) the component should be entirely removed before performing the broken part welding operation. Doing so allows the weld to be performed without going through an unnecessarily deep hole making the operation easier and more likely to be successful.
If you don't have access to a MIG welder a drill guide bushing can be useful to assure the drill is centered and doesn't wander off to the side of the broken bolt stud. I often make my own drill guide bushings like these for special jobs:
Slow low pressure drilling at first to allow the drill to get started on the uneven broken end of the stud/bolt helps keep the drill from being pushed off center. Drill as deep as possible followed by a larger drill size but not so large that the threads are endangered. If the part is broken off close enough to the surface and the hole drilled large enough sometimes the remaining bolt/stud threads are all that's left in the hole and they can be pulled out like unwinding a spring from the threads in the casting. In the case of using an extractor, often hollowing out the broken part will relax the outward tension on the threads allowing easier removal with an extractor of some type. My preferred extractors are the straight fluted type with no taper. I have used a quality set by Snap-On that is nearly identical to this one:
After using the recommended drill size the are driven into the hole and cut into the broken part causing minimal outward pressure on the threads.
Note: I have no experience with the set linked above nor can I vouch for it's quality although it is considerably less expensive than the Snap-On set.