Don't drill!!!!!!!!!!!!!!!!!!!
Put a washer over the area of the broken stud. Make sure the hole in the washer is centered over the broken stud. Using a MIG welder, weld in the hole directing your arc at the broken stud.
The stud can be broken off below the surface - it doesn't matter! After the washer is welded to the stud, weld a nut to the washer...the same way. Look at my pictures above!!!
Here's the proof that it works great!!

7710166-079.JPG (68 downloads)