Oh boy, as a retired Toolmaker the experience removing broken fasteners and taps from blind holes has always been a cause of anxiety, frustration, and occasional victory.
A hardened steel bolt in a soft aluminum casting is a special thrill.
My first go to in this case would be to try and file any ragged edges that protrude as flat as possible, use a pr$%k punch to mark the center of the bolt, follow with a center punch for a lead in for a left handed drill near the root diameter of the thread. Be sure to run the drill motor in reverse as the left handed drill will not cut going clockwise. If you have been very good, the drill will catch a little and the bolt will want to spin out on the threads, only push hard enough to make the drill cut, if it does indeed catch be ready to allow the bolt to back out. If that does not work, you will at least have a hole in the center of the bolt, and you can use a "Thread Extractor" (EZ-out) why they call them easy is a mystery to me, but here you are, I hold mine in a tap handle so that I can keep pressure on the center and try to be sure it digs into the bad fastener and does not slip.
Not fixed yet? Oh boy.
Now you sneak up on the root diameter of the thread and when it is only the last bit holding on you take a small punch, or a small sharp cape chisel and try to collapse one side of the threads in enough to grab it with a needle nose pliers and wiggle and twist to remove the stubborn remains, then using a thread chaser, or a dull tap clean the remaining threads in the casting, blow out with brake cleaner with straw, and be very careful when torquing the new bolt to stay at the low end of the torque spec.
If that does not work look up "Heli-coil" thread repair inserts. Last stop on the road sometimes.
