after many years in automotive and many a broken bolt- i have a couple of ways to remove broken bolts and studs. to me it's not proper to drill and tap- best way is to leave the hole with threads intact. i would only drill to tap size as a last resort!Ive been searching around and havent found a answer anywhere. what do i gotta do if the screw broke off on the head for the exhaust. it broke off when i was about 3/4 out
first- if it's not broken yet- make sure you have a torch handy. if you heat the area around the seized bolt then spray lube the expansion/contraction will break the grip on the bolt. many stubborn cases require several tries with heat and lube. i've gotten many a rusted bolt out this way. patience is critical. keep working it back and forth slowly between lubes until it works out.
once broken- the easiest way- buy left hand drill bits. they're fluted in the opposite direction for left hand drilling. when the bit grabs it will spin the offending bolt right out of the hole. most cases this works.
most stubborn case- hold a washer on over the broken bolt. weld the washer to the bolt. be careful to center the weld and not weld the washer to the sides of the hole. then weld a nut onto the washer. this, in combination with the heat/lube process, has gotten more bolts out of heads without pulling the head than any other method. it is truly a lost art! with practice it can be a very valuable skill. i once took 9 broken exhaust manifold bolts out of a 454 chevy(5 on one side and 4 on the other) without pulling either head. was an all day project- but pulling the heads would've taken me a week!
lost all hope of removing the bolt- drill, tap, helicoil. by this point if you don't get something to work you're screwed!
hope maybe this helps- or at least give an idea of what's needed. good luck and have patience!