It can be difficult removing a broken bolt or stud that is recessed in a deep hole as there are not many techniques to remove the bolts. Before attempting to remove any bolt, it is a good idea to shock the bolt first, then apply some heat and finally some spray penetrant (once it is cool). Drilling out the bolt is one of the few options that will work in this scenario. In this video I show two techniques that could potentially work when a bolt is broken in a deep hole or a bolt is sheared in an aluminium component.
Some more videos that might be of interest are-
How to remove a rounded Allen head bolt- https://www.youtube.com/watch?v=WDOWPekMX44
How to remove a stripped screw- https://www.youtube.com/watch?v=_mTFQbaT3Zc
How to remove a broken bolt- https://www.youtube.com/watch?v=_R1b8niX13w
How to remove a rounded nut or bolt- https://www.youtube.com/watch?v=R5d0Bgvjmlk
Screw extractors | Easyouts - https://www.youtube.com/watch?v=SMrDYJvY0Ts
Removing a broken bolt using a welder- https://www.youtube.com/watch?v=aRrz-cphBY4
Remove a broken bolt using a left handed drill bit- https://www.youtube.com/watch?v=FYvaPbX1sT4