Retired machinist here......
1. File top of broken bolt to create a flat area 2/3 the size of the bolt.
2. carefully use a centerpunch to mark the bolt's center for drilling.
3. select a drill that is 1/8 " or bigger
4. Heat the area if it's an option
5. start your first drill while things are warm at medium speed and enough pressure to produce a chip.
6. correct the location if you happen to be slightly of center by angleing the drilll (no side pressure).
7. clear chips often.
8. use sulfur based oil
or a wax candle to lube the drill (not lubricating oil
which will decrease the drills bite).
9. If the bolt is short, drill through, reheat and fill with penetrating oil. (liquid wrench)
10. Heat again and open the hole to 2/3 bolt size.
11. soak with penetrating oil and insert a non tapered punch and start tapping with a light hammer. The shock waves will allow the oil to penerate more easily.
12. Lightly tap your easy-out to set it in the bolt. Hard taps will expand it!
13. Heat the area around the bolt while rotating the easy-out.
14. If this proves unsuccessful, you'll need to drill the bolt out to "just under ithe minimum diameter of the thread and chase the remaining threads out with a similar threaded tap.
15. If things get ugly and you destroy the threads, you'll need to use thread inserts to save the project