I have drilled out and threaded several in my experience. Most, in fact.
Best done using the head twisted off and then grind the stub down so it's nearly level with the exhaust manifold surface. This gives you a "true location" for the bolt.
With the extent of the bolt diameter revealed then with a sharp punch "centerpunch" what you feel is the centerline of the broken bolt. Then starting with a 1/16" drill, drill a hole until you feel it "drop" into the void below the broken piece.
Then in 1/16" increments, expand the hole until nearly the root diameter of the thread. IIRC, the bolts are 5/16 which has a root diameter of No. F drill or 0.257. The nearest fractional size is 17/64 which is 0.2656. I would drill this to 1/4" or 0.250 and try to pick out any thread you can reach. Then try for No F drill and pick out more.
If you can get a circle or two of thread clear THEN try putting a 5/16-18 tap and re-tap the hole. More than likely the tap will follow the previous threads removing only what remains of the original bolt. Finish up with a "bottoming" tap which can be made from a ground-off standard plug tap.
If you're a little off-center in your drilling, approaching the final thread root diameter "gently" will help preserve as much as you can of the original female thread. Being off center means you "clip off" one side of the thread form but enough will remain on the other side to allow full bolting. AND clipping off one side CAN make it easier to "pick-out" the remains of the bolt.
Use penetrating oil generously during this process.
In drilling process and coming up perhaps half way to the root diameter, I might try an 'easy out' simply as part of the exercise. I can't for the life of me remember the last time it worked, however. Easy-Outs are a nice marketing name, but don't describe well the heartbreak of breaking one off in the hole.
Hope this helps.
Joe K